2005 Prius coolant reaches 230-240F when driving on highway

Is the Torque instrument calibrated correctly?
Have you used other measuring instruments for comparison?
A faulty measuring instrument can show the temperature on the surface of Mars and inside a volcano vent at the same time.

 

Yeah what are you using to measure this temperature where are you getting this reading from TIS Toyota software freeze frame data etc? You actually should be able to smell this kind of temperature when you open the hood You don't generally forget it I got four generation twos here I couldn't make that kind of boiling coffee water if I wanted to and I'm in the 100° weather in the southeast United States for five six months of year. I'd have to put a piece of cardboard in front of the radiator for 40 minutes possibly more. And what else is happening at this 2:40 if you whip over on the side of the road or pull back into your driveway and whip the hood up what's happening The two main hoses to your radiator for the engine should be so tight you can't even touch the hose because of the heat and it is harder than a 700C bicycle wheel pumped up for a road race holy Jesus so there must be something seriously wrong if you've done all this other work. If you back the fans on the back of the radiator away from the radiator with this kind of heat going on and you run your hand across the core of the radiator relatively quickly is there a big cool spot in the middle? This is a thing. If so your radiator core is plugged and your radiator fluid is going around that plug the cold spot and the hot areas around the radiator or where the water's trying to get past the plugged area very common You need to find out about this quickly before you burn up your engine I would say you've got a hold up probably from stop leak in the bottom core of the radiator assembly that handles the ice engine this has nothing to do with your inverter or any of that My guess would be the radiator core is plugged jump that out or change that core and probably the problems gone In a shop you could take a water hose and make a fitting and connect it to the radiator hose and a container and see what happens but if you feel the cold spot in the middle of your core in the midst of this then you know where your problem was My buddy at the radiator shop diagnoses this hundreds of times a year in the southeast United States on all kinds of vehicles that need coolant to not overheat.

 

Has anyone ever put any additive into your cooling system (ie. stop leak, gasket sealer)?

 

Don't assume a new radiator cap is a good one. I ordered one from Gates for the wife's '98 accord and when pressure tested it would not open. That combined with another cooling system failure could have been catastrophic. Have it pressure tested. Autozone and other places like that loan out cooling system pressure testers which can be used for this. There was a really steep deposit though, something like $250.

I suppose it is possible the temperature sensor is out of spec and the values you read are wrong. Honestly, that seems like a very unlikely scenario.

Maybe the water pump is not pumping very well? Is the belt still on, not slipping, no coolant seeping out?

None of the cooling hoses kinked or pinched? (Like somebody worked on the car and left a clamp on.)

Presumably the thermostat tested good. If this is one of those cars where the thermostat can be put in wrong (upside down or backwards) verify that it is in the correct orientation.

Following up on Biomed1's comment, what does the coolant smell like? Stop leak smells horrible. If it has a bright yellow/green tint and glows under an ultraviolet light that would be another indicator that there was at some point a coolant leakage problem.

Does the heat work? If the core was leaking they might have tried stop leak, and if that didn't do it, bypassed it altogether.

Both upper and lower hoses get hot?

How long have you had this car? Is the grill blocked? People sometimes do that to get better MPG in the winter, but it would cause problems like you are seeing in the summer.

Look through the grill, is the condenser totally clogged with mud or leaves or something like that? That would also act like a grill block.

Sure you got all the air out of the system? Jacked up the front of the car and ran it with the cap off the radiator for quite a while? Turned the heat on full while doing that? Afterwards it should have needed a little more coolant after driving for a couple of days, as the last few bubbles came out.

Are the hoses to/from the three way valve on correctly? I have a vague recollection of people putting those on wrong and making a hash of the cooling system circulation.

If none of that turns up anything you will probably have to work your way around the cooling system systematically to try and find where the problem is.