Depends on what you define as heat. Is the heat excessive? Has the gear lube ever been changed before? If you work it hard, which i'm sure we all do, it will get warm. I change the lube every year in the trucks, whether it needs it or not.
Only my opinion
i change my oil every 2,ooo to and the filter every other time but have not done any of the others yet was going to but ford said they would recomened it next year and that i would be fine for this season
If it is hot enough to touch with your hand you are fine. Changing the gear oil is a good idea and synthetic is the way to go.
GM makes a great additive, called "Limited Slip Axle Lubricant Additive" (part #1052358) It is about $6 or $7 for a 4 oz. bottle. This stuff is really worth adding. A local transmission rebuilder told me to use it on a manual transmission that I was about to have him rebuild as it was shifting hard and grinding. I couldn't beleive it worked so well. The transmission shifted perfect after that. I now put it in all of my rear axles and manual transmissions as part of my maintenence schedule.