The heat recovery works in both directions. Of course, that does not mean active cooling. Only an air conditioner can do that. Simplified example:
Inside 23 degrees / outside 30 degrees.
Exhaust air therefore 23 degrees / supply air 30 degrees.
Now comes the heat exchanger. It cools (actually exchanges) the temperature of the outgoing air with the supply air. It just doesn't work 100%. That's why you don't get supply air at 23 degrees but at 24 degrees. The numbers are made up by me, I cannot provide actual figures. But it is meant to illustrate the function.
This means that the house gradually warms up. Because it is not active cooling. Just slower than if you open the window in between and let in 30 degrees. Because you shouldn't keep the windows closed all day, that becomes stuffy with the airtight building envelopes.
The second effect is the summer bypass. It ensures that according to defined parameters the controlled residential ventilation system recognizes that the supply air is not warmed by the exhaust air during the cool summer nights. So instead of reheating the nightly 18 degrees to the otherwise desired 21 degrees, the air bypasses the heat exchanger, so that the effect described above lasts longer. Overall, this leads to a house (with proper shading in addition) warming up more slowly and staying longer within comfortable temperature ranges than a comparable house without controlled residential ventilation.
Of course, this has limits. If we have a heat period of over 3 weeks during which the nights are also 26 degrees, this no longer works.