I searched the threads and found diff answers about belts...

No belt driven water pump. No belts of any descriptions, if I'm not mistaken. Any warning lights? If so there will likely be codes, which will help.

Any recent coolant change? Residual air pockets might result overheat?

 

It does have a crank pulley. But I have no idea why, since it has no belts. Does anyone know why it has the pulley?

First thing I'd do in this case is to get an OBD2 reader to see what the various temp readings are, directly from the ECU, vs. just going off the light coming on.

 

Do both radiator hoses feel nice and hot after the engine has warmed up to temp? Strong heat out of the heater? See coolant circulating through the plastic bottle (again, only with engine up to temp)?

 

My guess, and it is just a guess, is that as the engine also comes in non hybrid versions that do have belts, Toyota decided that one part number was easier than two.

Toyota ZR engine - Wikipedia mentions that it is related to the 2ZR-FE.

 

If you did search, how many belts does your car have?

 

how many miles on her?

 

Yes, this is more important for this case than most other cases where Bisco reflexively asks. If the previous suggestions don't lead to anything, then I'd be thinking of the clogged EGR problem that has hit so many Gen3 Prii, and miles will be a hint.

 

i'm just naturally curious