When we bought our carriers, we made sure to buy ones that look okay with our decor. So we leave them out around the house with the doors open all the time. The kitties will use them to play in, sleep in, or when they want privacy from the other kitties (we have a herd of 5).
Somehow, they know when it's time to go to the vet. Sometimes we have issues catching them but they go into the carrier pretty easily. If we can catch them when they're napping, it's a cinch.
But none like the ride in the car. They meow, whine, howl, etc. the entire trip to the vet. Once they are out of the car, they'll usually quiet down. When they don't, it's so embarrassing to be sitting in the waiting room with a howling carrier.
Great idea using the seat heater! What a nice treat for kitty.