What is the most optimal latitude on Earth for the generation of extreme maximum temperatures?
The places that get the hottest temperatures are close to the equator but not necessarily on the equator. They will be low lying places, perhaps below sea level, and 'enjoying' a continental climate. For the record books, they will also need to be places where a climatologist passes through at the right time to measure it. I see you mention some record temperatures in your question, but I don't remember off hand what the absolute world record temperature is. It won't be far short of 55 C, but what amazes me is how the people who measured such temperatures survived to tell the tale. The atmosphere must have been very dry. From the point of view of human wellbeing, in high humidity temperatures well short of world record don't feel well short, and are almost as dangerous.