If i were you eventhu the CEL is not on i would check it with the obd2 and see if you get any code the CEL light bulb can be bad sometimes. The coolant temperature sensor, the brake light switch can cause the car to go on limp mode as well. Your car is running really hot. I would start with the cheapest stuff witch is probably a thermostat and a coolant temperature sensor and a brake light switch, but first see if you get any code with an obd2.