It would have been nice if there had been a bit more video telling us which pet had claimed the prime spot in front of the space heater first.
I'm guessing the dog took the bed, slightly back from the heater. The cat took the spot in between, then the dog decided to stretch out and found the cat there and the pussycat wasn't going to move out of the way, so it became a pillow. The cat looked like it was trying to decide if the indignity of being made a dog pillow was worth leaving the warm spot and getting dog stink on his/her fur.
Only near the end does the cat finally close its eyes. With that almost human look of exasperation at 1:07 ("why me!"), I'd like to guess it was just short of annoyance.
I'm guessing the dog took the bed, slightly back from the heater. The cat took the spot in between, then the dog decided to stretch out and found the cat there and the pussycat wasn't going to move out of the way, so it became a pillow. The cat looked like it was trying to decide if the indignity of being made a dog pillow was worth leaving the warm spot and getting dog stink on his/her fur.
We'll never know.