If you restart your Mac go into the Spotlight search (magnifying glass) icon on the top-right corner bring up "Activity Monitor" by typing that in. On the "CPU" tab of Activity Monitor there is a graph at the bottom. It will contain your Idle %. On a fresh Mac with nothing running in the background (and not running league of legends I would expect your Mac to show that it is 95% idle, your fans to be virtually inaudible and it to be barely warm.
The lower your Idle % means more things are running. As you get down to 80% idle your fan should still be very gentle and your Mac only modestly warm, it should be only down around 60% roughly or lower Idle % that your fans should be running much faster.
Checking this out will make sure there is no legitimate software problem causing your CPU to run hot.
A game like league of legends will be running your Mac at near full capacity which will cause the fans to be loud and the system to run hot. Playing on a hard solid surface (like a desk) versus a soft surface like a bed or a couch will help.
Once you determine there's no software problem and no fan hardware problem you can get a powered USB cooling pad *with fans on the bottom* to keep your MacBook cooler if you like playing lots of heavy duty gaming but it's important to determine there's no hardware or software problem first.
You mentioned the slight grinding. If it only does that as it shuts off that's probably not a problem. If it ever makes any grinding sound while running though, that's a problem.
