Actually the claim was that the global poor are close to the equator. Given how little motivation I have to even move when it's very hot, and how moving is required to generate wealth, and how recently A/C was invented, it's probably not totally a coincidence.
I mean it’s pretty easily explained by the Industrial Revolution starting in Europe, which is very far north. The explanation that heat induces laziness is a bit suspect given that in older eras many of the most prosperous civilizations were near the equator. (Egypt, Sumeria, the Persians, Indus River Valley Civilizations, etc.)
I don't really know how to compare the prosperity of ancient Sumeria and Denmark, but ancient Rome did conquer ancient Egypt and the reverse never happened.
The fact that the industrial revolution occurred far away from the equator supports the notion that the tropics are not conducive to progress/wealth. Granted it's a small sample size. Hard to re-run history dozens of time to get more data unfortunately.
After the industrial revolution, Europeans proceeded to colonize much of the planet, such as both Americas, but it wasn't Venezuela or Ecuador that became a global superpower.
Within the Eastern hemisphere, Japan, Korea, China seem to have done better at progress and wealth as compared to Southeast Asia. Granted Singapore and Hong Kong have done well lately, but maybe because of a/c - https://www.vox.com/2015/3/23/8278085/singapore-lee-kuan-yew...
But yea Mercator isn't the problem.