I have a '06 Toyota Highlander that blows hot air from the vents when the controls are in the following positions: Temperature anywhere in the cool to cold range, fan on at any speed, diverter in any position, A/C OFF.
The air comes out hot after I make a sharp turn in either direction.
If I turn the fan off I get fresh, cool air from the vents regardless of the turns.
It sounds to be like your blend door needs attention - its in the ductwork and controls where the air comes from (heater core, AC, neither). This is often a fairly substantial interior/dashboard disassembly job.
If that were the case, there would be complications with the A/C too. The A/C works fine, as does the heat. This only happens when trying to get fresh air.
I also agree with the blend door possibly being the problem. The way a lot of Asian imports are set-up, the coolant flow to the heater core is controlled by a vacuum motor with a vacuum switch connected to the ventilation controls. The coolant flow to the core is only turned on when the fan is turned on. With the fan off, the switch cuts the coolant flow, and the heater core stays cool. If the blend door is flapping during turns, this could explain the symptoms your experiencing.
That’s not what your original post said so maybe a better description is in order. Either way though, you have a “door” problem. There will be a blend door and then there is probably another for the fresh air/recirc. It sounds like one or both of those doors is not working right. Often these doors are controlled by engine vacuum. I don’t know how the Highlander’s is set up but you can start by inspecting vacuum lines beginning under the hood and ending up under the dash.
Locate the hot water hose that feeds the heater. It usually starts near the thermostat and runs to the heater core. Install a shut-off valve in this line (they make nice cable controlled ones you can operate from the cabin, or just a common in-line valve of the proper size). This will give you 100% control of the heater and remove that source of heat from under your dash, always a benefit during hot weather…
Uses servo motors for air mix and fresh air. See picture.