Yeah, do not sleep on the stomach! It puts way too much pressure on the vertebra & discs!
Sleep on your back with pillows under your knees and perhaps some rolled up towels or a rolled up pillow under your neck. The ideal thing would be to get a cervical pillow. You can get those at health stores or some pharmacy's carry them too. They are usually "U" shaped. If you want to sleep on your sides, you need to put pillows between your knees and make sure you have enough pillows under your head to keep your spine aligned.
Who knew that sleeping could get so complicated, huh?
If any back pain continues, I wouldn't use JUST heat -- I'd alternate heat & ice, using each for 20 minutes every 2 hours. Don't use heat continuously. I wish you the very best. Keep us posted on what happens & take care. Hugs, Lee