It would be helpful for you to more specifically define "tropical areas" as challenges to metabolic rate and evaporation will such things as elevation.  Here are a series of papers on birds that you might find helpful in answering your question.

Thanks for you answer. but my problem is about exertion of this heat from our body. in cold areas, temperature gradient is the key for descending of our temperature and stabilizing it. in hot and dry areas, the evaporation can be the key for exertion of heat produced in basal metabolic.

But in humid and hot areas, like tropical areas, none of these (evaporation and temperature gradient don't exist). so the temperature of our body will increase and ...!!!

Surely, a mechanism must be in action, because there is life in these areas.

As far as I know, there is no different formula to calulate BMR in cold or hot places.

The difference between thaose examples is not basal metabolic. For basal we calculate energy expenditure for 24 h in a room at warm temperature, not cold, not hot.

To avoid temperature increase, body has its mechanisms as sweat, etc. 

But despite thats would mean an increase in expenditure, we do not count it in practice to design diets.