Blinking red temperature light/engine hard to start

hard time turning on. It'll start, and then turn right off unless I give it enough gas then it stays on. After driving for about 5 minutes, the red temperature light blinks. When this happened about two months ago, it didn't want to start up again. The coolant and oil were both full, which makes me think there is something at large wrong with the car. Once I let the engine cool down for about an hour, the light stays off, the engine turns on, and the car is fine like nothing happened. I am not sure if I should take it into the dealer or an independent mechanic. Any ideas on the diagnosis?
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Megan

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