heat won't help now , in fact it might make it worst, ....it will help later .
this type of injury unfortunately takes a long time to heal, but it won't stop you from working out.....just avoid squating for now. medicine (pills or cream) can help with the pain. and in the future , if your goal is to build muscle and look good , there is no need to squat heavy at all, unless your goal is powerlifting. I can squat a lot , but never train with more than 165 lbs and rarely go up to 220, my legs got much bigger since i decided to use low weight and high reps. Squats and deadlifts are great exercises if done properly and avoiding heavyweights and they can be your worst enemy if you go heavy, because the slightest mistake in your technique can cost you a lot..and anybody can make such a mistake.
As you start feeling better there are some exercises that will strengthen your back muscles around your vertebrates and in the middle of your back.