What cooler to you have?
It's totally normal for raceroom to run cooler. The crucial fact here is that acc is finally a sim that is making at least a little use of modern mukticore CPUs.
Raceroom basically on 2 big threads internally. Meaning in theory, a 3 core cpu would be plenty enough (2 for the big threads, 1 for the little threads).
This also means that me, with 4 cores + HT am seeing stuck fps although my cpu is at about 40% load and my gpu at 60%.
It's the "single thread performance limit". The game simply doesn't have enough threads to use the whole cpu.
Acc uses 3 big threads and a 4th kinda big thread.
Together with the rest (multiple little threads), it means that a 4 core cpu can be fully used. Way more than raceroom can!
Sadly instead of seeing the fps go into the 200's if you lower the graphic settings or resolution, acc needs the whole cpu to run basic 60-90 fps.
This leads to a fully loaded cpu while playing acc and therefore a lot higher temperatures.
Now 90° with the fan at maximum isn't great. Especially since acc doesn't even "redlines" the cpu. You'll probably see it fluctuating between 70-99% cpu load.
When checking if the fan is okay for a system it's always recommended to do a so called "stress test".
Intel burn, prime95, 3d Mark (cpu tests), running cinebench.
Or my favorite: the cpu stress test coming with msi kombustor. Kombustor is a great tool for overclocking the graphics card and the cpu stress tool is very simple, easy and shows the same temperatures like rendering a video or multi core games do.
Anyway, to sum up your problem:
Your cooler isn't good enough for your system. It's like telling a car owner "yeah if you go over 3k rpm or 150 kph, your engine will overheat".
Now raceroom is like City traffic. It's okay.
Acc is Autobahn.
Imo something like a cooler should always be able to take full load. Maximum temps I would tolerate would be 80° in acc and 87° in stress tests.
I personally have a very very bad pc case with one of the best Air coolers (le grand macho rt).
I'm reaching 74°c in acc and 78°c in stress tests.
It's not really known what too high temps really do to a cpu. Many say it would accelerate degeneration though. So at some point it will either fail or you'll have to run at lower GHz.
Anyway what case, cooler and case Fans do you have and how are they set up?
Maybe we can find something without you buying stuff