I think the Mac Mini was meant to be a desktop computer that does most things adequately well, but with the ability to push its limits once in a while without dying too soon. But I think due to the attractive pricing, people are buying the Minis to do more than what it was meant to do; things like a Mac Pro or an iMac Pro would do better in sustained continuous work without going to the temperature extremes. I mean, there's really no room in the Mini to provide good airflow as it would a Mac Pro or an iMac Pro can. Small space heats up faster than a bigger space with more fans.
I own a Mac Mini 2011 as well as the Macbook Air and had pushed these 2 computers to the brink that both had thermal shutdowns while rendering a few times already. So my solution was actually this year to get a Mac Pro and with this computer, it never shutdown doing the same things that it would with the Mini. Secondly, I removed the base black round cover of the mini and then attached a fan that improves airflow and sucks warm air and pushes it out through the rear external vents. So basically, I have 2 vents (one from the Mini's fan and the other from this external fan). It helped lowered the temperature down to 70˚C where it would go all the way to 90-100˚C before it would shutdown. Same with the Macbook Air with 3 base fans to cool it down while rendering a 4K video. I also use MacsFanControl to customize fan speed for these workloads. I hope to keep both Mini and the Air working a little while longer and I don't think too much heat @ 90˚C to 100˚C over hours and hours of continuous rendering are good for these machines over days, months and year. But they are way more cost effective way to get the jobs done I suppose.
I use Protools with my Mini and even at lighter loads, it would just heat up crazy even when its internal fan just got cleaned and the vents cleaned. Without the external fan setup and the plug-ins I'm running, it would shutdown which increases my frustration especially when you are in the middle of bouncing audio and the whole piece gets corrupted.