I don't have any experience with Toyota trucks, however the condition sounds like a temperature sensitive rich mixture condition.
My immediate assumption would be any of the several types of sensors modern computer control vehicles usually have to read temperature to adjust the mixture accordingly.
IAT usually isn't given enough sway over the tuning tables to make that kind of a difference so I'm going to guess it's an ECT. The engine coolant temp sensor. If it has one, I can't imagine it wouldn't.
Older chevys (GenII TBI) have that fail quite a lot. On those I know if you unplug the sensor and the condition improves then it's the sensor at fault. Although I'm sure the correct method would be to look up whatever the resistance at the senor would be and check it with a multimeter. Depending on how Toyota set the setup the computer the test of unplugging it may not apply.
Now if it's not that I suppose it could be a leaking injector, or an FPR. Something to that effect would be less temp sensitive and more persistent imo. It can't hurt to change the fuel filter and check fuel pressure though. Mainly because there is also a possibility that it's a lean condition.
Lastly, it could also be a clogged cat. Once again, the symptom of loss of engine power fits, but it shouldn't be temp sensitive.
