Is heat beneficial to help inflamed gum tissue as it is trying to heal?

Not especially: What was done or what is your situation that caused the inflamed gum tissue? Knowing that would help us answer your question more completely and accurately. One of the best ways to help things heal in general is to keep them clean, eat a healthy diet, avoid further irritation and get sufficient rest. If you have had recent dental treatment, ask your dentist for more specific advice.

Depends: If inflammation caused by infection, heat will just help the infection spread to other organ systems. Important to determine the cause of the inflammation before deciding on appropriate treatment. Would suggest that you see a gum specialist, a Periodontist, rather than trying to mask symptoms.