Weighing up the hemispheres: Everything tends to be bigger taller larger in the colder regions of the earth than in the steamy hot regions because a large body mass index allows them to function in climates that an smaller species would be having heart palpitations in when trying to build up to such body mass indexes.

I don't see a great deal of evidence to support this. The tropics are inhabited by elephants, giraffes, big cats, etc., but also small animals including insects, mammals, etc. Yet the very coldest regions are also inhabited by both very small and large organisms, e.g. large = polar bears, musk oxen, caribou, small = midges, mites, nematodes, etc.

I suppose your argument has some validity among endotherms (mammals and birds). Smaller endotherms need to keep their body temperature high in cooler climates by metabolizing a lot of food, often more than is available and so often spend long periods hibernating (e.g. bats, dormice, lemmings, etc.). But this does not always preclude them from cold climates, e.g. arctic lemmings.

I agree with Skeptic. In all regions there are large and small animals.