Yes, it has both in cab electric quick attach and a 120v engine block heater. The block heater plug is easily accessible inside the rear door.  The  JCB 300T is rated at 3000 lb capacity. Pro box weight varies but generally is around 2500 lb. The standard probox is 45" wide so, when picked up across the short side, the cg of the load should be about 24" from the mounting plate. I've been handling very wet 5x5 baleage bales that are heavier than that and with the cg a bit further forward.

The 300 T should have no problem with a 2500 lb pro box, picked up with forks across the shorter 45" side, as long as you are on fairly level and firm ground when up high. Carry it low if going down hill.  I would try lifting a pro box before you buy the machine to be sure.