OTC anti-inflammator. Tmj is something you may have temporarily or may have for a lifetime - but it goes in spurts, or "episodes". One episode will typically only last a day or so, or in severe cases a week or two at the very most! the best remedy to is have a customized bite guard made by your dentist to ensure you are not bruxing while you sleep, aggravating your TMJ muscles.
TMJ is name of joint. Your question is the same as asking if there are any home remedies for knee. The causes of TMJ dysfunction are numerous and varied. As with any joint, the best recipe for self- care is time, rest, ice, and anti-inflammatories. If the symtpoms don't resolve in 10-14 days, you will likely need professional help. See you dentist--especially if trained in treament of the tmj.
No absolute remedies. Common sense solutions may help. No chewing of gum, bagels, taffy and such. Limit jaw movements when possible, no opening super wide for hotdogs, hoagies, singing, etc. Ice applied for a few minutes and warm moist heat applied to area help some. A good exam is necessary to eliminate more serious problems that may be causing your "tmj" problems.