And also keep in mind, these things are also airtight, and are (mostly presumed to be) equipped to keep the pilot alive in the cockpit in case of a reactor breach that'd flood the outside with radiation. Also, you be thinking a tad too big - the Rad-Man doesn't have nearly enough energy to heat up a mech, it'd need a reactor itself.
Well, first off, just being "immune to radiation" usually refers to high-frequency radiation, like gamma rays, as well as having some resistance to alpha and beta particles. Lower frequency, like infared, micro, and radio waves, are usually able to pass through such protection. Hence why a concrete bunker may be "radiation proof" but you can still get a radio signal from inside.
Also, microwaves normally aren't damaging at all, except for a very specific set of wavelengths. Your standard microwave produces these wavelengths, and they have the unique property that they're able to impart vast quantities of energy to water. Hence, a glass cup won't get heated much in a microwave, even after a long time, but a cup filled with water will quickly reach boiling. Your microwave keeps this radiation inside by using a specific mesh (you know the little circles in the window?) which just happens to correspond with the size of the microwaves trying to get through. This interrupts the waves, keeping them safely inside. However, this mesh would not protect against higher frequency radiation (at least not much) because the mesh is the wrong size. Basically, you'd need the mech to be specifically armored against this type of microwave radiation, which isn't all that crazy, considering.
As to the power of the rad-man, you're thinking too big, Sean. You don't need much energy to boil the water in an average human brain, just a finely-tuned force.
Finally, something that's always bugged me, I don't see how it would be possible that any ship could have a cockpit the pilot could see through, that would also be immune to lasers. After all, it's just visible light. I mean, it would be possible to have a polarizing shield, but that could be countered by simply rotating the laser. And you couldn't get something in the way of the laser just as it's coming, because it's traveling at the speed of light, so there's no early detection possible, hence no active defense.
Remind me never to get in conversations about scifi tech again; I always over-think things.