the FCC "considers 50 watts to be the lowest power above which radiation must be considered [...]" for radio transmitters. in 1996.
further:
> Conversely, lower frequencies penetrate deeper; at 5.8 GHz (3.2 mm) the depth most of the energy is dissipated in the first millimeter of the skin; the 2.45 GHz frequency microwaves commonly used in microwave ovens can deliver energy deeper into the tissue; the generally accepted value is 17 mm for muscle tissue.
> The damage can be spread over a large area, when the source is a relatively distant energy radiator, or a very small (though possibly deep) area, when the body comes to a direct contact with the source (e.g. a wire or a connector pin).
note the microwave 2.45GHz part says frequency, not wattage, power, whatever. a home router's antenna's radome (or rubber duck or whatever) touching your arm will penetrate it quite far.
anyhow i've gotten RF burns before, just to see if it was BS or not, at real low wattage (around 1W at the terminal) and it leaves a discolored mark on your skin in a straight line between the contact points and feels like you got a small burn there. The frequency i "burned" myself with was ~145MHz.
This is all to say "it doesn't matter if it's ionizing, it still heats things up."
ETA:
> Frequencies considered especially dangerous occur where the human body can become resonant, at 35 MHz, 70 MHz, 80-100 MHz, 400 MHz, and 1 GHz