Not really. I do a lot of astrophotography with a DSLR, but use the DSLR effectively as a mirrorless camera. I also regularly wedge in filters that prevent use of the SLR mechanism anyway. Considering my total exposure times are regularly in excess of 2 hours, heating isn't really any different from mirrorless, and mirrorless would be a blessing for its versatility and simplicity.
The only real way to combat heat issues for exposures that long is a cooled sensor.