Revenue Recognition (Details) - USD ($) $ in Millions	12 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2020
Disaggregation of Revenue [Abstract]
Net sales	$ 2,050.1	$ 1,808.4	$ 1,975.5
Contract Balances [Abstract]
Contract assets	26.8	5.7
Contract liabilities	11.8	5.6
Increase in contract assets	21.1
Increase in contract liabilities	6.2
Liquid and Air-Cooled Automotive Businesses [Member] | Held for Sale [Member]
Contract Balances [Abstract]
Contract assets		7.1
Contract liabilities		2.9
Segment Total [Member]
Disaggregation of Revenue [Abstract]
Net sales	2,101.9	1,856.0	2,038.4
Segment Total [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	2,002.0	1,783.4	1,901.9
Segment Total [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	99.9	72.6	136.5
Segment Total [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	1,074.3	852.1	1,039.8
Segment Total [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	788.5	733.4	779.4
Segment Total [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	239.1	270.5	219.2
Segment Total [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	784.6	627.3	660.4
Segment Total [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	96.6	64.5	106.9
Segment Total [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	69.8	72.1	66.7
Segment Total [Member] | Commercial Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	334.2	264.8	323.7
Segment Total [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	336.6	264.1	253.9
Segment Total [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	370.0	455.7	508.8
Segment Total [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	110.1	107.5	118.0
BHVAC [Member]
Disaggregation of Revenue [Abstract]
Net sales	336.6	263.2	306.5
BHVAC [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	318.0	257.4	240.4
BHVAC [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	18.6	5.8	66.1
BHVAC [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	187.6	144.2	175.8
BHVAC [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	149.0	119.0	130.7
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	238.0	197.5	197.5
BHVAC [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	96.6	64.5	106.9
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	2.0	1.2	2.1
CIS [Member]
Disaggregation of Revenue [Abstract]
Net sales	627.5	512.4	541.1
CIS [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	580.9	472.5	501.5
CIS [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	46.6	39.9	39.6
CIS [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	336.9	268.7	309.2
CIS [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	262.7	199.2	186.5
CIS [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	27.9	44.5	45.4
CIS [Member] | Commercial HVAC&R [Member]
Disaggregation of Revenue [Abstract]
Net sales	546.6	429.8	462.9
CIS [Member] | Data Center Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	0.0	0.0	0.0
CIS [Member] | Industrial Cooling [Member]
Disaggregation of Revenue [Abstract]
Net sales	69.8	72.1	66.7
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	11.1	10.5	11.5
HDE [Member]
Disaggregation of Revenue [Abstract]
Net sales	824.5	682.1	745.9
HDE [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	789.8	655.2	715.1
HDE [Member] | Products Transferred Over Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	34.7	26.9	30.8
HDE [Member] | Americas [Member]
Disaggregation of Revenue [Abstract]
Net sales	511.6	388.2	484.5
HDE [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	156.3	133.2	141.2
HDE [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	156.6	160.7	120.2
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	319.7	250.4	302.1
HDE [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	331.9	260.7	240.8
HDE [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	84.0	97.9	108.4
HDE [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	88.9	73.1	94.6
Automotive [Member]
Disaggregation of Revenue [Abstract]
Net sales	313.3	398.3	444.9
Automotive [Member] | Products Transferred at a Point in Time [Member]
Disaggregation of Revenue [Abstract]
Net sales	313.3	398.3	444.9
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	38.2	51.0	70.3
Automotive [Member] | Europe [Member]
Disaggregation of Revenue [Abstract]
Net sales	220.5	282.0	321.0
Automotive [Member] | Asia [Member]
Disaggregation of Revenue [Abstract]
Net sales	54.6	65.3	53.6
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	14.5	14.4	21.6
Automotive [Member] | Off-Highway [Member]
Disaggregation of Revenue [Abstract]
Net sales	4.7	3.4	13.1
Automotive [Member] | Automotive and Light Vehicle [Member]
Disaggregation of Revenue [Abstract]
Net sales	286.0	357.8	400.4
Automotive [Member] | Other [Member]
Disaggregation of Revenue [Abstract]
Net sales	$ 8.1	$ 22.7	$ 9.8
Maximum [Member]
Revenue Recognition [Abstract]
Period of time after billing when payment is received	90 days