I like the way the current set drive, but I'm having a hard time controlling the temperature of the front tires and the car keep kicking out under braking after driving for a while. What can I try to do?

it's kinda hard without a set and/or replay to see where improvements can be made... but if you're having temp problems, you might want to switch up tire compound.

Also try bumping up the front tire pressures.

As for the corner entry oversteer, the rear end might be too stiff so you could try lowering the ARBs (anti roll bars) in cockpit when you feel the oversteer kicking in. You could also try less Stiffness at the rear.

Lower the rear tyre pressuares a bit.