My phone keeps overheating really fast

Cell phones don't have internal fans like a computer and rely heavily on design for airflow and cooling. Apple is really uptight about having your phone fixed at a non-apple tech and doesn't make its replacement parts that readily available; you can find "compatible" parts but using those or the non-apple tech technically voids any warranty on the device. So, although the guys in the mall mean well and are probably doing a good job, they are also most likely not using apple replacement parts and the parts they do use could interfere with the airflow of the original design.

Aside from that, did you get a new case after the screen fix? Some cases smother phones more than others, obstructing airflow.