Yes you will distort the plate by having interference fit pins in the edges; maybe not to the tolerances I work with but certainly to your tolerances.
However unless you have machined the plate optically flat the inherent surface inaccuracies will be comparable to the distortion from the pins so it may be immaterial.
Heating the plate could introduce a can of worms. Getting it hot enough to open the holes up far enough to let the pins simply fall in will probably relieve stresses and cause distortion.
Regarding the differential expansion if you are going hot enough for this to be a factor again you are probably relieving stresses in the aluminum.
If you rigidly glue your mirror onto the plate and then heat it you have created a bi-material strip, it will bend like crazy.
Why not have a size for size or even a very small clearance and use Loctite?