Mac Mini powerful enough to play any 1080p movie? I have a Mac Mini (Mid 2011) with 2,3 GHz Intel Core i5 8 GB RAM with SSD, that I use to watch videos. The machine is great in all respects, except if I play 1080p encoded with H265 or VP9, the fan goes to full speed (and CPU tops around 100%). 1080p at H264 plays fine without fan noise.

What is the minimum upgrade that will let me play any current 1080p file without audible fan noise? I realise the problem is caused by a slow CPU / lack of GPU support, which means replacing the entire unit, which I am willing to do. So which (second hand) Mac Mini is strong enough for this?
You won't do that with a Mac Mini. The latest Mac Mini uses a Haswell cpu (core gen4) which provides acceleration for H.264/AVC 8-bit, VC-1, MPEG2 and JPEG.

Additionally:

H.265 = HEVC = MPEG-H Part 2 = standard

x265 = encoder (and not the only one which exist).