Revenue Recognition, Disaggregation of Revenue (Details) - USD ($) $ in Millions	12 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2019
Disaggregation of Revenue [Abstract]
Net sales	$ 1,808.4	$ 1,975.5	$ 2,212.7
Contract Balances [Abstract]
Contract assets	5.7	21.7
Contract liabilities	5.6	5.6
Decrease in contract assets	(16.0)
Liquid and Air-Cooled Automotive Businesses [Member]
Contract Balances [Abstract]
Contract assets	7.1
Liquid and Air-Cooled Automotive Businesses [Member] | Held for Sale [Member]
Contract Balances [Abstract]
Contract liabilities	2.9
Total Segments [Member]
Disaggregation of Revenue [Abstract]
Net sales	1,853.0	2,035.8	2,281.2
Total Segments [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	1,780.4	1,899.3	2,101.5
Total Segments [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	72.6	136.5	179.7
Total Segments [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	851.1	1,039.8	1,152.5
Total Segments [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	731.4	776.8	879.1
Total Segments [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	270.5	219.2	249.6
Total Segments [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	602.2	639.7	674.0
Total Segments [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	106.0	150.2	187.0
Total Segments [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	55.4	43.5	47.8
Total Segments [Member] | Commercial Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	264.8	323.7	387.6
Total Segments [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	264.1	253.9	314.1
Total Segments [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	455.7	508.8	542.8
Total Segments [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	104.8	116.0	127.9
BHVAC [Member]
Disaggregation of Revenue [Abstract]
Net sales	240.6	221.1	212.4
BHVAC [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	240.6	221.1	212.4
BHVAC [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
BHVAC [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	144.2	139.1	124.9
BHVAC [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	96.4	82.0	87.5
BHVAC [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
BHVAC [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	181.6	176.6	167.7
BHVAC [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	58.7	42.7	41.3
BHVAC [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
BHVAC [Member] | Commercial Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
BHVAC [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
BHVAC [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
BHVAC [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.3	1.8	3.4
CIS [Member]
Disaggregation of Revenue [Abstract]
Net sales	532.0	623.9	707.6
CIS [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	486.3	518.2	571.1
CIS [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	45.7	105.7	136.5
CIS [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	267.7	345.9	413.6
CIS [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	219.8	232.6	244.8
CIS [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	44.5	45.4	49.2
CIS [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	420.6	463.1	506.3
CIS [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	47.3	107.5	145.7
CIS [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	55.4	43.5	47.8
CIS [Member] | Commercial Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
CIS [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
CIS [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
CIS [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	8.7	9.8	7.8
HDE [Member]
Disaggregation of Revenue [Abstract]
Net sales	682.1	745.9	872.3
HDE [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	655.2	715.1	829.1
HDE [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	26.9	30.8	43.2
HDE [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	388.2	484.5	543.0
HDE [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	133.2	141.2	177.4
HDE [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	160.7	120.2	151.9
HDE [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
HDE [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
HDE [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
HDE [Member] | Commercial Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	250.4	302.1	352.6
HDE [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	260.7	240.8	298.1
HDE [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	97.9	108.4	116.7
HDE [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	73.1	94.6	104.9
Automotive [Member]
Disaggregation of Revenue [Abstract]
Net sales	398.3	444.9	488.9
Automotive [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	398.3	444.9	488.9
Automotive [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
Automotive [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	51.0	70.3	71.0
Automotive [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	282.0	321.0	369.4
Automotive [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	65.3	53.6	48.5
Automotive [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
Automotive [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
Automotive [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
Automotive [Member] | Commercial Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	14.4	21.6	35.0
Automotive [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	3.4	13.1	16.0
Automotive [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	357.8	400.4	426.1
Automotive [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	$ 22.7	$ 9.8	$ 11.8
Maximum [Member]
Revenue Recognition [Abstract]
Period of time after billing when payment is received	90 days