Oh yeah- another quick and easy "while you are in there" which gave me ENDLESS trouble on my 944. May or may not apply to your situation.
Buy a new radiator cap! Especially on my older 944, the rubber gasket was bad, and it was not making a good seal, therefore system not pressurizing, causing air to collect in the system.
I did everything. radiator, pump, ts, hoses, 10,000 "purges" of air in the system, not including a lifetime of fans/relays checking/ rechecking. Bit fingernails off worrying about HG.
A stupid freaking radiator cap (actually the cap on the coolant reservoir on the 944), but you get the idea.
Infact- if I had the same symptoms on a 944 (and they were almost identical to yours), I would order the TS and the radiator cap first (both cheap)- burp the system, and install the radiator cap only and try it out to prevent even having to get under the car. If it didn't work, I wouldn't tell anyone
and move onto the TS, but that's exactly what I would do. My cap (seal) was about 20 years old when it died