I moved to a very hot country two months ago afer living in a cold one for 21 years. is it normal for my period to change (come 6 days early)?

That can happen: A big change in environment can alter one's hormonal balance and change the timing of a cycle or two, but of course, these changes are not predictable. Things that can influence hormones may include the number of daylight hours, amount of emotional stress, amount of physical work compared to sleep and rest, amounts and types of food eaten, etc... But cycle changes could also be just a coincidence.