I have Ubuntu 16.04.1 LTS on this low power SoC board Asrock N3150DC-ITX with N3150 CPU:
http://ark.intel.com/products/87258/Intel-Celeron-Processor-N3150-2M-Cache-up-to-2_08-GHz

According to https://support.plex.tv/hc/en-us/articles/201774043-What-kind-of-CPU-do-I-need-for-my-Server- (see The Guideline) I quote:
Very roughly speaking, for a single full-transcode of a video, the following PassMark scores are a good guideline for a requirement:
1080p/10Mbps: 2000 PassMark
720p/4Mbps: 1500 PassMark
I found my CPU on one of Plex's pointed charts:
http://cpubenchmark.net/midlow_range_cpus.html
When you click on CPU's link in the chart it will get you to http://cpubenchmark.net/cpu.php?cpu=Intel+Celeron+N3150+%40+1.60GHz&id=2546 from where I quote:
Description:  Socket: FCBGA1170
Clockspeed: 1.6 GHz
Turbo Speed: 2.1 GHz
No of Cores: 4
Max TDP: 6 W
Average CPU Mark 1693
With only 1693 mark you'll say there's no way this lazy CPU to transcode a HEVC ... but there is!

You'll have to mount a RAM directory in /etc/fstab e.g.:
tmpfs /var/plex-transcoding-temporary-dir tmpfs defaults,relatime,mode=1777,size=99G
This line will mount 99 GB of your RAM (surely much less 99 GB) to /var/plex-transcoding-temporary-dir directory which then you'll have to configure as the Plex's transcoder temporary directory.

I have 16 GB RAM but while transcoding a 1080p HVEC I only need less 2 GB RAM while also keeping in RAM my Ubuntu 16.04 desktop with mysql, sickrage, couchpotato, transmission, nginx and other.

Plex uses a maximum transcoding cache of 100 MB so I guess it won't use more than 100 MB of your RAM for transcoding. Plex won't transcode a movie larger than your tmpfs RAM directory size so I declare 99 GB just to be sure to transcode any possible movie.

My transcoding options:
Transcoder quality: automatic
Transcoder temporary directory: /var/plex-transcoding-temporary-dir
Background transcoding x264 preset: faster
Maximum simultaneous video transcode: 1

Amazing, isn't it?