CAI make higher idle, Affect gas mileage? Options

[mgnt232]

So when starting a car in a cold environment, the rpms are higher while warming up, then they will go down to normal. But Ive noticed recently (first winter with my CAI) that the rpms will never drop to where they would normally be (a little below 1k) with the temp a little warmer outside
My intake its basically outside my car, right underneath the drivers side directional (large opening with the invaderkit). And now the temps have been falling to like 20° or below recently. I can actually feel the intake (cone splash guard) and its freezing cold even after the car is warmed up.
Im wondering if its possible that the air its sucking in is "too" cold, to where the intake temp sensor would read as if the car is still not warmed up all the way (if that makes sense). Idk if it works like that, but my rpms last year always settled down after the car is warmed up but now, its always at like 1.3k, instead of like .8k (idle). Or if there is something else I should look into.
Also could this slightly affect mileage?