Driving home today, after about 10 minutes on the road in stop and go traffic, display read Engine Temperature High, or something to that effect. The temperature gauge was pinned to the high side. I was fortunately a few minutes from home. When I opened the hood the coolant reservoir was full and leaking from the cap. I let it cool down and then restarted and let it idle for a while, the cooling fan did come on eventually so I don't think thats the problem. Could this be due to the thermostat being stuck closed? I am thinking that the temperature sensor is OK since it was reading high.

Should I replace the thermostat as a first step? Thank you!