My 2014 Mazda 5 blows warm vent air when set to the coldest vent setting with the a/c turned off. I was able to get to the hot/cold air mix actuator thinking I had a malfunctioning unit which prevents the door from closing completely but it functioned correctly when I tested it. I even manually closed the vent door completely and there is still warm to hot air so there seems to be a leak in the door which allows warm air to bleed into the vent when cold air is set at max (without the a/c). When the a/c is on, there is no cold air. Has anyone else experienced this? Any solutions besides pulling the dash and removing the HVAC unit?

Now for the proposed solution. The heater hose is easily accessible under the hood so my thought is to cut the hose and add a shut-off valve to prevent coolant from entering the heater core during the summer months. I know this is a redneck solution but I believe it would take care of the problem as I believe the a/c would function better without the heat bleeding in as well. If I periodically open the valve to ensure coolant flows through to keep the heater core flushed, would there be any other potential problems to other cooling components such as the water pump?