Its no secret that cutting mats will over time develop a curl where the wheels run.
Most folks also know that a heat gun used carefully will soften the plastic
But then how do you very quickly get the curl out before the mat cools?
First step heat the mat only along the curved depression created where the wheels run. You heat both sides for best results but do the back side last.
Next quickly lay the mat sticky side up over the radiused edge on a countertop or table with that wheel path aligned right along that smooth radius edge and then pull the mat back and forth across the edge in the area you heated while pulling down on the mat edge that projects over the counter.
If you mat is warmed enough to soften the plastic it should only take 10 seconds or so to flatten it back out by working the curve back the other direction using the assistance of the edge of the table or counter top as an opposing force.