1999 Pontiac Grand Prix Prix Drive Car About 10 Mins First Starting Temp Light

I have a 1999 Grand Prix. When I drive my car about 10 mins when first starting my car my temp light comes on. I look at the temp gauge and it says that it is not over heating. Its doesn't even get a quarter of the way up. Since the light it on it switches to emergency mode. I have checked my coolant levels and found out it was low. I have added more coolant. Thinking that is why my temp light was coming on. After adding more coolant I was still having the same problem. Within 10 mins of driving my engine light would come on and but the gauge says its within normal temps. Is there something else that would be causing my temp light to come on? or why my car would be behaving like this.

I have also checked my oil level and that is normal as well.