Heat is not the problem.
The plasma inside the cells are reacting to the electromagnetic waves.
Like a grape in a microwave.
https://www.youtube.com/watch?v=wCrtk-pyP0I

The ions are conducting the electricity, which causes the enormous radiant plasma. The plasma inside the cells are ions contained in water and have a far less violent reaction.

In studies, we can indeed see that ions are pushed through membranes inside the cell, and are able to damage the cell. But this is only the surface of all the biochemistry that happening inside cells and the body.

These hazards are not looked at by standards that were introduced by the navy, that used big radar systems that made some people get radar-injuries. That way the injuries seemed avoided. These standards were never changed to deal with bio-electrochemistry and long term exposure.

For peer reviewed research and other info see: http://www.microwavenews.com