Bless you for adopting a heartworm positive dog. I have never had one, but I was told that the dog has to be inactive. Being active can kill the dog. It is a very curable disease. Rescues successfully treat dogs all the time.
Here is a link to the American Heartworm Society. If you can't find your answers there and have a specific question, I will be glad to contact someone else in the rescue I volunteer for and see what they say.
American Heartworm Society - Heartworm Positive Dogs