https://www.blackmesasource.com/
scroll down to the bottom
"Get instant access and start playing over 8-12 hours of single player campaign and multiplayer deathmatch. Xen is not part of the Early Access release, but will be included as a free update when ready."
There isn't really a Black Mesa: Source. That was just the name of the mod for a long time before it had its first official release, Source is simply the name of the engine it and HL2 run on. It always just released as Black Mesa. The actual difference is that there's the free mod version of the game which is how they released it back in 2012 without any updates and the paid version which has been improved drastically and is about the get an update that adds the final Xen chapter to the game. That one's currently in beta and should release in a month or so (excluding Valve Time. Fingers crossed).
All that aside, 4 gigs of ram is probably not enough for the paid version. Try the mod and see how it runs. I played it on the shittiest laptop of all time back then and somehow managed to beat it. If it runs badly just play the original (as in Half Life, not Half Life: Source). It's old but still plays great.
All I could find real quick was these maps, from 2013. No idea how they work on the CU3 build: https://www.moddb.com/mods/black-mesa-on-a-rail-uncut/downloads/on-a-rail-uncut-full-beta
> quickly cooks my CPU to the point that my motherboard starts to complain
That kind of thing shouldn't happen at all. It sounds like you have a cooling issue that I would highly recommend looking into. Run Open Hardware Monitor to see the temperatures and fan RPMs.
I was running BMS on a laptop from the same year as the FX-6300 and never had any trouble with temperatures.