Segment and Geographic Information, Net Sales, Gross Profit, and Operating Income by Segment (Details) $ in Millions		12 Months Ended
		Mar. 31, 2023 Segment	Mar. 31, 2022 USD ($)	Mar. 31, 2021 USD ($)	Mar. 31, 2020 USD ($)
Segment and Geographic Information [Abstract]
Net sales			$ 2,050.1	$ 1,808.4	$ 1,975.5
Gross profit			$ 309.3	$ 293.4	$ 307.5
Gross profit (% of sales)			15.10%	16.20%	15.60%
Operating income (loss)			$ 119.2	$ (97.7)	$ 37.9
Strategic review alternatives cost			2.6	6.6	39.2
Segment Total [Member]
Segment and Geographic Information [Abstract]
Net sales			2,101.9	1,856.0	2,038.4
BHVAC [Member]
Segment and Geographic Information [Abstract]
Net sales			336.6	263.2	306.5
CIS [Member]
Segment and Geographic Information [Abstract]
Net sales			627.5	512.4	541.1
HDE [Member]
Segment and Geographic Information [Abstract]
Net sales			824.5	682.1	745.9
Automotive [Member]
Segment and Geographic Information [Abstract]
Net sales			313.3	398.3	444.9
Operating Segments [Member]
Segment and Geographic Information [Abstract]
Net sales			2,050.1	1,808.4	1,975.5
Gross profit			$ 308.6	$ 293.9	$ 309.5
Gross profit (% of sales)			14.70%	15.80%	15.20%
Operating income (loss)			$ 151.0	$ (58.7)	$ 97.1
Operating Segments [Member] | BHVAC [Member]
Segment and Geographic Information [Abstract]
Net sales			334.6	262.0	304.4
Gross profit			$ 93.6	$ 85.3	$ 100.2
Gross profit (% of sales)			27.80%	32.40%	32.70%
Operating income (loss)			$ 45.7	$ 45.2	$ 58.2
Operating Segments [Member] | CIS [Member]
Segment and Geographic Information [Abstract]
Net sales			619.5	506.4	535.1
Gross profit			$ 88.5	$ 64.2	$ 64.3
Gross profit (% of sales)			14.10%	12.50%	11.90%
Operating income (loss)			$ 35.3	$ 10.2	$ 11.1
Operating Segments [Member] | HDE [Member]
Segment and Geographic Information [Abstract]
Net sales			787.9	648.3	693.8
Gross profit			$ 87.2	$ 88.4	$ 96.6
Gross profit (% of sales)			10.60%	13.00%	13.00%
Operating income (loss)			$ 34.6	$ 36.8	$ 37.8
Operating Segments [Member] | Automotive [Member]
Segment and Geographic Information [Abstract]
Net sales			308.1	391.7	442.2
Gross profit			$ 39.3	$ 56.0	$ 48.4
Gross profit (% of sales)			12.50%	14.10%	10.90%
Operating income (loss)			$ 35.4	$ (150.9)	$ (10.0)
Corporate and Eliminations [Member]
Segment and Geographic Information [Abstract]
Net sales			(51.8)	(47.6)	(62.9)
Gross profit			$ 0.7	$ (0.5)	$ (2.0)
Gross profit (% of sales)			0.00%	0.00%	0.00%
Operating income (loss)	[1]		$ (31.8)	$ (39.0)	$ (59.2)
Inter-segment Sales [Member]
Segment and Geographic Information [Abstract]
Net sales			51.8	47.6	62.9
Inter-segment Sales [Member] | BHVAC [Member]
Segment and Geographic Information [Abstract]
Net sales			2.0	1.2	2.1
Inter-segment Sales [Member] | CIS [Member]
Segment and Geographic Information [Abstract]
Net sales			8.0	6.0	6.0
Inter-segment Sales [Member] | HDE [Member]
Segment and Geographic Information [Abstract]
Net sales			36.6	33.8	52.1
Inter-segment Sales [Member] | Automotive [Member]
Segment and Geographic Information [Abstract]
Net sales			$ 5.2	$ 6.6	$ 2.7
Plan [Member]
Segment and Geographic Information [Abstract]
Number of operating segments | Segment		2

[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 2022, 2021, and 2020, the Company recorded $2.6 million, $6.6 million, and $39.2 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.