Heat is not a problem. Wax only liquifies at something close to 200 degrees F. The biggest problem with wax is proper application. You have to melt it in a double boiler and leave the chain in there long enough to heat the chain completely through so that the wax (and usually you add PTFE as a 2 or 3% additive ) completely saturates the chain. If you remove the chain and it is hardening between the links the chain is still cold. Properly, the chain remains perfectly clean and when it starts getting so that when you rub it with a finger and you're getting black marks it is time to clean the chain again and re-apply. This is usually a couple of months if you do a good job and ride several times a week,
Cleaning a waxed chain can be done several ways. You can use gasoline which is usually easiest and then clean it thoroughly with soap and water. There is this stuff called SuperClean I think it's called, that you can get from your local automotive supply store. In is a SUPER soap in a purple plastic half gallon or gallon container. If you WAVE the capped bottle at the chain it cleans it. Be absolutely certain to use rubber gloves with you use this stuff because it will wash all of the oils out of your skin and even your fingernails which will then crack and break easily. Putting any chain in this stuff and leaving it covered with up to 50:50 water would clean up anything. It only takes a couple of hours without any effort on your part other than shaking the pan now and again.
ALWAYS test for chain stretch before waxing since the wax can hide the stretch. Never let that SuperClean touch your paint or your anodized aluminum wheels. It dulls them almost instantly.