I have done a lot of mini testing. to aid in cooling externally large fans are needed. op says he does very heavy gaming so 75c can and will happen. handbrake can push a mini to 90c. been there done that.
I have used 15 or twenty external fans and you can drop the internal temp 4 to 8c with correct fan use. one of the best fans was a 6 inch industrial fan runs ac I used a variable transformer and can run the fan with over 225 cfm of air . here is a link to it
http://www.galco.com/scripts/cgiip.exe/wa/wcat/itemdtl.htm?pnum=W2S130-AA03-01-EBM
just give it 90 volts ac instead of 120 it runs slow and quiet it will move a lot of air at 90 volts about 150cfm. i used to put in t7600 intel cpus on 2007 minis I used a lot of fans to control temps just in case the new cpu was over heating. buying one of these can cost under 25 dollars on ebay but you need an ac voltage transformer and you need build a case. if he gets over 90cfm tossed at the bottom of the mini it will help.
edit :
of course make sure the mini has been dusted internally