Is my Mac Mini's fan okay? I replaced the HDD with a hybrid HDD/SSD about a week ago, following iFixit's guide for doing so. However, when putting it back together, I stripped one of the connectors on the fan.

My Mini gets really hot, so it makes me think the fan isn't working all the way, if at all. At the same time, my office doesn't have insulation (and it's on the second floor of my apartment) so it gets really hot. I have a fan on now, facing me and the Mini and it feels better, just a bit warm.

I just want to know if I am stressing too much, or if there is reason for concern.
Depending on the model year of the Mac mini, you could run Apples hardware diagnostics if supported.

Shutdown your Mac mini.  Turn back on and press and hold the keys: option + D during the grey screen before the Apple logo.

If asked join a network and let it boot into the Apple hardware test.  This will tell you if the fan is reporting an error along with other hardware tests.