Yes but modify
I agree with many of the answers here.
An acute injury to the mandible or face should be iced. I often recommend a frozen bag of peas or popcorn kernels so that the cold can adhere with contours of the face and jaw. Ten minutes on, the 10 off is usually adequate. Don't leave the cold on for too long of a period at a time. Moist heat is usually used for injuries and pain that has lingered.