overheat

The air conditioning compressor defiantly puts load on the engine (and takes away power resulting in losses in fuel economy as well). The additional load on the engine does increase engine running temperature. Before any other investigation check to see that the head gasket is not blown. This is best done by having a test done called a "block check' where the engine is run up to operating temperature and then the cooling system is checked for the presence of carbon monoxide (CO2) in the cooling system. CO2 is a by-product of combustion and is only in the cooling system if the cylinder head gasket is not sealing or the cylinder head is cracked. It is a big job to do a head gasket in a Previa. I will send you an article I wrote about the cooling system that shows how a block check is done. I will send it to the email address you posted this question to Repairpal from.

After experiencing some overheating, I recently self drained & flushed my 1993 Previa's radiator and reservoir tank with interesting results. First, I removed the top plastic air duct intake cover. Then I removed the radiator reservoir tank. After unscrewing the bottom radiator drain plug to drain coolant, I ran a yard water hose (with on/off hand grip for control) from the top radiator inlet hole and flushed out the old coolant. The interesting part came when I completely cleaned and flushed the coolant reservoir tank with a the yard water hose. I noticed that one or two of the three inlet/outlet nozzles had been clogged with debris and/or coolant sealant. So I cleared the reservoir's thin nozzles with a Q-tip and thin ice pick or screwdriver. It appeared that the reservoir tank had been clogged which made the cooling system inefficient, especially during warm weather with the AC on. To flush out the old coolant from the engine, I ran the yard water hose from top radiator hose with the engine one for about 1 minute. Eventually I saw old water/coolant flush out from the hoses that connects to the reservoir tank (which had been removed.) After 45 minutes of draining, cleaning, flushing, I hooked everything back up and refilled the radiator with fresh coolant. Be careful when removing the hoses... the nozzles, nipples, or hose connection tips can easily be broken if the rubber hoses are pulled the wrong way. For now it seems the radiator is keeping cool. If your temperature needle is showing up hot past the middle mark, try flushing out the reservoir tank to make the cooling system more efficient. It may be clogged because 3 of the 4 holes are very small and can easily get clogged with old coolant, debris, dirt and/or sealant.

warm up the engine with the heater on when the gauge reads half of way turn the fan on and rev the engine until hot air is coming out the heater core is mounted higher than the engine so all the air in the system needs to come the radiator cap needs to loose

I noticed one item missing in your repair list. It happens to be the one item that fixed my exact same symptoms back in '91 with a '77 Camaro. Radiator cap. Took 2000 miles and a radiator flush in Theadore Roosevelt Park in North Dakota. (Bison 10 feet from my legs!!). In desparation went to Chevy in Portland OR. and bought a cap. I was happy. Insidently I just returned from the same trip with a '93 Previa 3 days ago with the same symptoms. First thing I replaced was the cap. Didn't change a thing. This time it was a radiator. Exact same symptoms. If it ain't one thing it's something else! Also make sure you do the procedure in Answer #3. Dealers will verify this.