My truck runs a little warmer when it Regens but that's expected. Never had an issue with overheating tho. The DPF is what heats up at Regen the DEF is sprayed into the DPF to remove particulate buildup. Do you get a check engine light or overheating warning on the dash?
I has issues with mine when I got the cheap ****** from Amazon. LASFIT is the best for led swap built in resistors, no fault codes and they are BRIGHT AF. They are a little pricey but well worth it. Good luck