The recent heat wave in India saw more than 2,500 deaths, the fifth-deadliest heat wave on record. Here's the outgoing longwave radiation (OLR) measured over Asia during that time (May 15-27), measured by CERES. (Note: lighter regions are hotter.)
OLR depends on more than just the temperature of the surface -- like humidity and cloud cover -- so you can't just convert the OLRs to temperatures via the Stefan-Boltzmann law. But these differences are much bigger than I would have expected.