Why did you replace the proximity sensor? Was this related to a problem?
There are a couple of things that could be wrong here. You don't mention if the "warm" replacement screen works otherwise. I'll assume it does. You may have a defective screen or the connectors are not seated properly.
Open your device and go through this guide to insure you have done everything correctly. The FPC connectors are delicate and should "snap" when properly seated. Check them to insure they aren't damaged.
If the screen is still warm after you re-install it, try your old screen if it stills works to see if the warmth is specific to your replacement screen or not.
If the problem only follows the replacement screen, contact the seller and get a refund. Look for a reputable supplier like iFixit as they have great warranty service.