This morning I went to the barn to take Lilly's leg wrap off and allow her leg to "cool" during the day. Her leg, however, was substantially less warm today compared to yesterday and past days. So when I went out before work to check the temperature and wrap her back up, the leg pretty much felt the same as it had this morning.
I called and spoke with my vet and she is glad that the leg is cooler today. Her main concern is with Lilly's soundness, so unless she starts favoring that leg again, I'll just keep monitoring the temperature. She said there should be some heat in the leg because of the inflammation and that's just what it's going to do for the next month or two.