Why do different aircraft have different maximum operating temperatures?
There are a few different things going on here. For the best answer, see this blog post.

To summarize his points, there's a combination of factors:


The Bombardiers simply aren't certified at those temperatures.
Their combination of small wings and small jet engines makes high temperatures particularly problematic for them. With the air density decreasing as the temperature rises the wings get less lift and the engines suck in less oxygen. The bigger jets have larger wings and bigger engines which make up for their larger weight so they can fly while the regional jets can't.


So to answer your question ("Is this solely due to the size of the aircraft, or is it a difference of manufacturer?"): Yes