Consider Madeira which is a very relaxing place with a one year old, although it is not clear to me what you might regard as hot. Assuming you live in the UK then anything above 23 degrees or so is described in the media as hot and people complain about oppressive heat indoors even before the temperature reaches such dizzy heights. At that rate you could consider almost anywhere on the Mediterranean for daily maxima (early October). However, paradoxically, the British seem to want their money's worth and presumably be brought close to death with temperatures above 27 degrees on holiday. In October you are unlikely to find that sort of temperature in the northern hemisphere except in the middle east or further afield (out of your price range).