an Option:  You could always lay some Granite tiles in there.. maybe a checkerboard pattern.. Galaxy Black, with White.  lay down some Nu-heat.. electric underfloor matting, as used in restrooms and such.. only heat the areas you want heated.
I have tiled garage floors with granite and its not too cost involved if your a DIY.
You just need to know how to lay down the electric matting, and scuff prep the floor for it to stick.   
beats tearing out your concrete.  
 
 
overlays would not be thick enough for the heating. 
there's also the snap in style plastic floors.. not sure what R value you get from them. 
good luck.