Segment and Geographic Information, Net Sales, Gross Profit, and Operating Income by Segment (Details) - USD ($) $ in Millions		12 Months Ended
		Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2019
Segment and Geographic Information [Abstract]
Net sales		$ 1,808.4	$ 1,975.5	$ 2,212.7
Gross profit		$ 293.4	$ 307.5	$ 365.5
Gross profit (% of sales)		16.20%	15.60%	16.50%
Operating (loss) income		$ (97.7)	$ 37.9	$ 109.7
Strategic review alternatives cost		6.6	39.2	7.1
BHVAC [Member]
Segment and Geographic Information [Abstract]
Net sales		240.6	221.1	212.4
CIS [Member]
Segment and Geographic Information [Abstract]
Net sales		532.0	623.9	707.6
HDE [Member]
Segment and Geographic Information [Abstract]
Net sales		682.1	745.9	872.3
Automotive [Member]
Segment and Geographic Information [Abstract]
Net sales		398.3	444.9	488.9
Total Segments [Member]
Segment and Geographic Information [Abstract]
Net sales		1,853.0	2,035.8	2,281.2
Operating Segments [Member]
Segment and Geographic Information [Abstract]
Net sales		1,808.4	1,975.5	2,212.7
Gross profit		$ 293.9	$ 309.4	$ 365.1
Gross profit (% of sales)		15.90%	15.20%	16.00%
Operating (loss) income		$ (58.7)	$ 97.1	$ 144.9
Operating Segments [Member] | BHVAC [Member]
Segment and Geographic Information [Abstract]
Net sales		240.3	219.4	209.1
Gross profit		$ 83.0	$ 71.5	$ 63.4
Gross profit (% of sales)		34.50%	32.30%	29.90%
Operating (loss) income		$ 47.2	$ 36.4	$ 26.9
Operating Segments [Member] | CIS [Member]
Segment and Geographic Information [Abstract]
Net sales		528.1	620.1	704.7
Gross profit		$ 66.5	$ 92.9	$ 114.9
Gross profit (% of sales)		12.50%	14.90%	16.20%
Operating (loss) income		$ 8.2	$ 32.9	$ 53.4
Operating Segments [Member] | HDE [Member]
Segment and Geographic Information [Abstract]
Net sales		648.3	693.8	811.8
Gross profit		$ 88.4	$ 96.6	$ 127.8
Gross profit (% of sales)		13.00%	13.00%	14.70%
Operating (loss) income		$ 36.8	$ 37.8	$ 65.0
Operating Segments [Member] | Automotive [Member]
Segment and Geographic Information [Abstract]
Net sales		391.7	442.2	487.1
Gross profit		$ 56.0	$ 48.4	$ 59.0
Gross profit (% of sales)		14.10%	10.90%	12.10%
Operating (loss) income		$ (150.9)	$ (10.0)	$ (0.4)
Corporate and Eliminations [Member]
Segment and Geographic Information [Abstract]
Net sales		(44.6)	(60.3)	(68.5)
Gross profit		$ (0.5)	$ (1.9)	$ 0.4
Gross profit (% of sales)		0.00%	0.00%	0.00%
Operating (loss) income	[1]	$ (39.0)	$ (59.2)	$ (35.2)
Inter-segment Sales [Member]
Segment and Geographic Information [Abstract]
Net sales		44.6	60.3	68.5
Inter-segment Sales [Member] | BHVAC [Member]
Segment and Geographic Information [Abstract]
Net sales		0.3	1.7	3.3
Inter-segment Sales [Member] | CIS [Member]
Segment and Geographic Information [Abstract]
Net sales		3.9	3.8	2.9
Inter-segment Sales [Member] | HDE [Member]
Segment and Geographic Information [Abstract]
Net sales		33.8	52.1	60.5
Inter-segment Sales [Member] | Automotive [Member]
Segment and Geographic Information [Abstract]
Net sales		$ 6.6	$ 2.7	$ 1.8

[1] The operating loss for Corporate includes certain research and development costs, legal, finance and other general corporate and central services expenses, and other costs that are either not directly attributable to an operating segment or not considered when management evaluates segment performance. During fiscal 2021, 2020 and 2019, the Company recorded $6.6 million, $39.2 million, and $7.1 million respectively, of costs directly associated with its review of strategic alternatives for the liquid-and air-cooled automotive businesses, including costs to separate and prepare the underlying businesses for potential sale.