Sheepskin is not too hot. Air can circulate in the fibers if you keep the pad groomed and clean. Sheepskin provides a little cushion too, where the square pads provide none. Square pads are made for fashion and to keep the bottom of your saddle clean, that's it.
Square pads are ONLY acceptable in shows in Jumpers, Cross Country, and Dressage. They should not be used in Hunters or Equitation. Only a shaped pad or sheepskin half pad, both in white or very pale "natural" should be used in Hunter classes. You can use real sheepskin, wool, or synthetic fleece.