Reportable Business Segments - Schedule of Error Corrections and Prior Period Adjustments (Details) - USD ($) $ in Millions	3 Months Ended									12 Months Ended
	Mar. 31, 2023	Dec. 31, 2022	Sep. 30, 2022	Jun. 30, 2022	Mar. 31, 2022	Dec. 31, 2021	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2022	Dec. 31, 2021
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales	$ 1,049.4	$ 1,093.8	$ 1,244.9	$ 1,366.3	$ 1,013.4	$ 964.8	$ 1,059.9	$ 1,239.0	$ 930.5	$ 4,718.4	$ 4,194.1
Total segment profit	141.7	132.2	189.3	229.8	114.6	101.9	164.8	221.6	115.7	665.8	603.9
Cost of goods sold	(742.8)				(745.2)
As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		1,093.8	1,244.9	1,366.3	1,013.4	964.8	1,059.9	1,239.0	930.5	4,718.4	4,194.1
Total segment profit		132.2	189.3	229.8	114.6	101.9	164.8	221.6	115.7	665.8	603.9
Residential
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales	681.0	703.4	835.3	977.5	682.2	620.3	711.0	838.0	606.3	3,198.3	2,775.6
Total segment profit	111.1	119.2	153.8	216.3	107.6	110.3	144.0	189.7	96.4	596.9	540.3
Residential | As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		703.4	835.3	977.5	682.2	620.3	711.0	838.0	606.3	3,198.3	2,775.6
Total segment profit		119.2	153.8	216.3	107.6	110.3	144.0	189.7	96.4	596.9	540.3
Commercial
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales	308.7	327.2	352.3	327.4	279.5	286.3	292.7	335.0	274.8	1,286.4	1,188.8
Total segment profit	50.0	45.6	52.4	41.2	23.8	29.8	36.3	58.9	39.6	163.0	164.6
Commercial | As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		240.5	252.9	219.6	187.7	201.4	211.5	252.8	199.2	900.7	864.8
Total segment profit		27.9	29.6	17.2	6.3	15.6	22.6	45.3	27.4	80.9	110.9
Refrigeration
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Total segment profit		0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Refrigeration | As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		149.9	156.7	169.2	143.5	143.1	137.4	148.2	125.0	619.4	553.7
Total segment profit		18.8	22.4	23.4	14.1	13.2	14.5	13.5	7.9	78.8	49.1
Corporate & Other
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales	59.7	63.2	57.3	61.4	51.7	58.2	56.2	66.0	49.4	233.7	229.7
Total segment profit	$ (19.4)	(32.6)	(16.9)	(27.7)	(16.8)	(38.2)	(15.5)	(27.0)	(20.3)	(94.1)	(101.0)
Corporate & Other | As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Total segment profit		(33.7)	(16.5)	(27.1)	(13.4)	(37.2)	(16.3)	(26.9)	(16.0)	(90.8)	(96.4)
Corporate Segment
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Cost of goods sold		(33.7)	(16.5)	(27.1)	(13.4)	(37.2)	(16.3)	(26.9)	(16.0)	(90.8)	(96.4)
Corporate Segment | As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Cost of goods sold		(33.7)	(16.5)	(27.1)	(13.4)	(37.2)	(16.3)	(26.9)	(16.0)	(90.8)	(96.4)
Other Segments
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		63.2	57.3	61.4	51.7	58.2	56.2	66.0	49.4	233.7	229.7
Total segment profit		1.1	(0.4)	(0.6)	(3.4)	(1.0)	0.8	(0.1)	(4.3)	(3.3)	(4.6)
Other Segments | As Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Net sales		0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Total segment profit		$ 0.0	$ 0.0	$ 0.0	$ 0.0	$ 0.0	$ 0.0	$ 0.0	$ 0.0	$ 0.0	$ 0.0