Welcome to the Pain Mangement Forum. I am sorry to hear about you hip pain. It is one of the most sites for pain, although I am sure that does not help you feel better.
There are multiple reasons for hip pain. One of the most common is trochanter bursitis. It is the largest bursea in our body and when it becomes inflamed it can be very painful. Heat can increase the swelling of surrounding tissue and make your pain increase, or certainly not ease it rather it is bursitis or not.
The symptom that does not fit is the decrease in pain with ambulation. Does it hurt to touch the area or rest on it? If not than that may also rule out bursitis. So one things of the many other condition the can either effect the hip. It is also possible that it is referred pain, meaning you feel pain in one location that actually originates from another. It is not unusual to have groin or low pelvic pain that is referred from the a joint problem.
You may have osteoarthritis of the hip joint. Pain running down the leg can be from the hip or could indicate a structural issue in the spine. Only imaging of the area will provide you with the correct answers.
I hope you will make an appointment with your PCP to find a solution to your pain. We will look forward to your updates. Best of luck to you and as always, take care.
Janet, I have sacroiliac disease and have nerve pain jumping from hip to hip, as well as sciatica. You could have pinched something in there, or somehow twisted your ilium - have you tried a chiropractor? I can sometimes stretch that stuff out, but for the most part I have to go to chiropractor. If you don't have one already talk to your friends and family and see if you can get a recomendation. And good luck.
Also, heat for the most part is a no no! Ice is the way to go, because that nice feeling heat draws blood to the site and increases inflammation. Believe me, I found that out the hard way.