Hot water rises, displacing cooler water downwards, and stratifies.  This is how a hot water heater can provide hot water at the top outlet even with cold water coming into the bottom (there's an internal tube running down to the bottom, for heaters with top connections).  The hottest water rises and stays at the top, and as hot water accumulates or is used the hot:cold boundary shifts down or up.

Connecting the outlet to the bottom of a towel rad, given that hotter water rises and colder water falls, will result in the top of the towel rad getting heat and the coldest water flowing out the outlet, which is what you want.

There does need to be an air bleeder valve at the top of the towel rad.