air intake door opens during acceleration

If you mean it switches to defrost mode while under acceleration, then switches back to the mode selected when you let off the gas, that is because the heater controls run on engine vacuum. That vacuum goes down during acceleration or increased load. For safety, the mode doors are spring-loaded to go to the defrost position when vacuum is lost, such as from a broken vacuum hose. Your feet might freeze but your windshield will be clear.

To overcome this, replace the vacuum check valve with one with a storage canister built in from the dealer. The old valve is about the size of a stack of three nickels and will be found near the center of the firewall, below the windshield under the hood. The replacement is about two inches long and 1 1/2" wide.