Well they both do really. 5 Watts of UV absorbed and 5Watts of infrared absorbed are the same amount of heat.
IR tends to be more associated with heat because warm things emit more blackbody radiation in the infrared range. Making something hotter can shift the peak blackbody frequency higher into the visible light range, and even into ultraviolet and beyond, but at those temperatures things tend to be on fire.
The greenhouse effect works because glass (or greenhouse gasses in the case of the earth) absorbs infrared, keeping heat that would normally be lost to the outside via blackbody radiation from escaping. The actual source of heat in the first place is full spectrum light from the sun which includes uv, and visible light.
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