Is it safe to apply heat to my belly while pregnant?

No not advisable. No heat or heating padsor those shakeup packs should go on your belly while pregnant and if you are having belly pain or discomfort please call your OB as you need to be evaluated.
Yes it is. Yes, there is so much tissue and fluid between your skin and your baby that it would be next to impossible to hurt your baby with anything hot (or cold) you could put on your tummy. Even when people accidentally burn their abdomen with, say, hot grease, there is no harm done to their baby on the way.