This is such a good topic, I need to write about it in the blogs, thanks for asking this important question. I just transcribed this very conversation we had on our most recent Tripawd Talk Radio podcast, Veterinary Rehab Benefits for Three Legged Dogs, with Lisa Saez, PT, CCRT from Dalias Doggie Rehab, who tells us:

People are always very confused about this. Some people get stuck in the idea that you should ice the first 48 hours and then heat the area afterwards and that can be appropriate but it's not the only answer.

I generally tell people that heat is best if something is tight, it's sore, and ice is best if something is inflamed or swollen. But one things most people don't think of is ice is fabulous for muscle spasms. It will shut off or decrease the blood flow to that muscle and it actually helps to break up the spasm better. Whereas if you use heat on that sometimes it feels better intially but then the pain comes right back because you're sending blood to a spasming muscle.

How long to leave it on?

Generally for around 12-15 minutes is enough. Some dogs that tolerate either well, some dogs that tolerate one or the other. ...Many times there still is a gray area. I usually tell people that if one doesn't work, try the other. Unless something is severely inflamed and you don't want to use heat on it, in most instances there's not a problem of trying one or the other. I give a guideline of which to try first but it one doesn't work, try the other. There is a lot of individuality between dogs or even humans on which works better for each person or dogs.