Fan clutch is easiest, open hood and start engine, you should hear fan noise then it should get quieter, shut off engine, spin fan manually it should spin freely/easily.
Go drive the truck for the day, when you get home, engine warmed up, shut off the engine and pop the hood, spin the fan again, it should be tight, won't easily spin.
If this tests out then fan clutch is good.
If fan spins easily with engine/rad warmed up then replace it.
While the hood is open follow the heater hoses to the firewall there should be a valve or by-pass on the hoses.
A Valve will have an IN and OUT on one hose, the other hose will just run directly to the firewall heater core connection.
This type of set up usually can not cause the over heating you described, because the heater core is not part of the cooling system, i.e. the engine doesn't rely on coolant passing thru the core as part of the cooling, if it did then every time you closed the valve(like in the summer) the engine would over heat.
A By-pass setup will have 4 hose connections, two go to the engine and two go to the heater core, a by-pass setup is part of the cooling system.
The engine relies on coolant being circulated between the two engine hoses as part of the circulation pathway.
When you turn up the heat inside the cab the by-pass redirects flow to the core but circulation never changes in and out of the two engine hoses.
If the by-pass is restricting flow at certain "heat" settings then you would notice this as up and down temp gauge.
Since engine is warm already feel both engine hoses near the by-pass they should be the same temp, if one is cooler than the other you could have a blockage/restriction.
If there is no Valve or By-pass then heater core is part of the cooling system, feel both hoses at the firewall they should be the same temp if one is cooler then core could have blockage/restriction.
Last is the t-stat no real way to test this, if in doubt replace, they are cheap $15, 192-195 deg is what you want, WITH a "jiggle valve", yes that is a real thing, it is a hole in the t-stat plate that allows air out of the system when refilling, t-stat should be installed with jiggle valve at 12:00 position for best air release.
The hole has a metal pin in it that "jiggles" so hole can't be clogged over time.
A 160 or 180deg t-stat will cause your MPG to go down.