Think of it like this. The air coming through the vents when the system is set to fresh (not recirculated), has to be coming from outside of the car somewhere. That somewhere is no doubt from somewhere near the front of the car. The engine also happens to be at the front of the car. The engine happens to throw off a lot of heat.
I have also noticed on every car I have owned that when it is a nice cool day and you don't want to run the AC and you just have the vents on hoping to bring in some cool outside air, that the air coming through the vents is a little warmer than the outside air. You can tell this by putting your hand out the window and feeling how cool the outside air really is. The difference is more pronounced when sitting still as would be expected.
Your description of warmer or cooler is obviously subjective. We can't tell from the internet how much warmer you are talking about. There is a possibility that the mechanism that responds to the temperature knob you rotate is not operating correctly. That is it may not be closing off the warmed air completely on the cool side. Not sure how that could be checked.
I have also noticed on every car I have owned that when it is a nice cool day and you don't want to run the AC and you just have the vents on hoping to bring in some cool outside air, that the air coming through the vents is a little warmer than the outside air. You can tell this by putting your hand out the window and feeling how cool the outside air really is. The difference is more pronounced when sitting still as would be expected.
Your description of warmer or cooler is obviously subjective. We can't tell from the internet how much warmer you are talking about. There is a possibility that the mechanism that responds to the temperature knob you rotate is not operating correctly. That is it may not be closing off the warmed air completely on the cool side. Not sure how that could be checked.