Why is the Red Sea warmer at depth than other seas and oceans?

For one thing the Red sea is a pretty hot sea in a pretty hot place anyway.

Secondly, It has very saline deep water, partly because it largely dried out in prehistoric times and the salt deposited then still has not yet finished dissolving. Such brine is so dense that it does not float up through normal seawater even if it is hotter than the less salty water.

Thirdly, it has hydrothermal vents on its sea floor. They produce more salty, hot (very hot) water that does nothing to cool the deep water, even if their contribution is small.