Can't?
The above is hugely over-simplified.
Firstly, it's demonstrably true that heating changes the behaviour of living tissues. Your phone causes a small rise in temperature of tissue in your ear and brain. One of the likely changes is the speeding-up of undesirable biochemical reactions that create oxidative stresses. Such stresses are known to be carcinogenic. And warm-blooded mammalian metabolisms are fine-tuned for a tightly controlled operating temperature.
Secondly, and even more technical, there is a possible mechanism whereby microwave EM radiation may cause free radicals to flip into a different electronic configuration. Such altered radicals might escape being mopped up at the site of a biological reaction that is known to create them, and where nature has put suppression mechanisms in place. After migrating elsewhere in the cell, they go back to theoriginal state by emitting a quantum of microwave radiation, and cause damage. The theory is good; it would be verging on impossible to actually observe it in living issue.
Much better to assume "can", and ask "but does it"? More particularly, "does it to a significantly harmful extent"? I'd say for mobiles, "can" is proven, " does it" is uncertain, "harmful" almost certainly not, with a small lingering doubt in my mind for long calls in a maximum-transmit-power weak signal area.
BTW you're wrong about heating caused by sun on your head. It'll warm your scalp, but not your brain tissue (at least not up to the point you get heatstroke, which is deadly dangerous). Your blood circulation distributes heat from the sun through your entire body, like water-cooling a CPU, and your warm-blooded metabolism actively regulates your core temperature at a nominal 38.4C (+/- about one degree between individuals). Heatstroke is what happens when the regulation fails to cope. You die soon afterwards if someone can't cool you down.