Using gyrotrons for harvesting oil from shale

Speculation alert:

While studying the idea of beamed propulsion, I came across this video. I didn't put it up because it didn't seem all that interesting. However, this morning, I noticed an article on Instapundit about getting oil out of shale.

While it didn't mention gyrotrons, the idea of using gyrotrons for heating occurred to me. You see, there are those who don't believe this oil can be recovered economically.

However, that belief may be mistaken. If you use gyrotrons, you can selectively heat an area underneath the surface. That's interesting, because the shale is underneath the surface. Thus, you can heat up the shale underground, then harvest it.

What about the energy source to operate the gyrotrons?  I was thinking nuclear energy from molten salt reactors.  These reactors can be made small enough so that they can be moved from one location to another.  They wouldn't require water in order to produce the electricity.  And they could produce liquid fuels that can be used for transportation.