Preface: 2.0 running dual dell 36s
Appearance group oil temp gauge
Dakota Digital CHT under 3

So I'm about to delve into a tune up on this new teener I got. My first couple test runs were not to my liking and I need to find out why. Is the motor toast and needs a rebuild? It starts up and runs smooth so I wouldn't think no, but the head temps are running hotter than I'd like.

Check timing
Check valves
Check for items blocking cooling/missing - I believe part of the tin might be missing. The seals might also be missing. (would this cause high temps?)
Check carb jets - I believe PO said that are running rich to mask transition issues from idle to main jets
Check for cooling flaps and thermostat

Once all these things are checked and I am still not running cool, cruising at 65 mph on flat road with ambient temps around 70 where do I look?

Compression test and leak down will tell me if the engine needs a rebuild, but will that also tell me if it is running hot because it is not up to snuff to deliver the scoot power?

Let's say those also check out fine, would an external oil cooler mounted up front be enough to drop the head temps as well? Currently cruising just under 400 in 4th on the flat at 3500 RPM - temp gauge showing Over the M - so maybe ~250/260 if I have a late sender (car is a 74) Would the external cooler take that down to a manageable 210, but also bring the head temps down? Ideally I would like to see 210 oil temps and 350-375 cruising in 5th on a flat.

TL;DR - Does an external oil cooler also bring down head temps?

No, proper cooling and burn control the head temps. you're either lean or too much advance, or both. Proper sealing of cooling tin is a must, nothing should be missing.

You could also have a mouse nest, especially 3/4 if the head temp wire grommet is missing.

Thanks for the answer Mark.

I'll be checking the timing tonight. Hopefully also sealing up any holes I can until I get the proper seal/tin in place.