I slightly disagree. Radio waves can cause thermal heating in human tissue (close enough to the emitter, if there's high enough power),
Cell phones don't have enough power to cause significant heating.
It turns out that the body is very well adapted for cooling. The circulatory system is a good heat exchanger; it takes a lot of input to overload. Going outside on a 90 degree (F) day, maybe. Lying in the sun and absorbing a kilowatt per square meter, maybe. A one-watt (average transmit power) cell phone, no.
There is one exception to the fact that the cooling system of the body regulates the temperature, actually, the one place the blood vessels don't reach: the lens of the eye. You can't have blood vessels running through the eyeball, since it has to be transparent! If the scaremongers had been saying that cell phones caused glassblower's cataract, they would have had a mechanism. But that isn't the charge. (And, in any case, the power of a cell phone is just way too low to cause this-- you just don't get much heating from the 0.7 to 1 watt average transmit power of a cell phone to cause any damage. Don't stare into a red-hot furnace, though.)
[...] Although I haven't seen enough specific data on cellphones in this regard, I don't expect the effects to be significant.
You got it. The effect is not significant.