Face gets extremely red when biking in the cold ~5c, and then going indoors, due to temperature change maybe
You can't really wear anything to solve the problem you are describing.  If your face was cold, I'd recommend you purchase some sort of mask, however, that isn't your stated problem.  

When you exercise you generate heat, your body tries to channel that away by dilating blood vessels and sending that heat to the surface (your cheeks) where it can radiate away.  If you are cycling when it is cold, it can reinforce that effect since your body would be sending extra blood to try to heat your cold cheeks.  If you have generated a lot of heat cycling, then go indoors, you may also feel extra warm now that you have a lot of generated heat, are dressed for cold weather and in a warm room.  Again, flushed cheeks.  

I regularly bike to work in cold temperatures.  I start wearing a mask at 0F to protect both my lungs and face.  It's a very normal occurrence for me to have red cheeks up to an hour or so after arriving at work.  People sometimes comment, but I know it's normal for me.  I only start to worry if I get white patches (frost nip or no blood flow to areas that were over exposed).