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Question: Why is my car nearly overheating every time I drive?

I was in a car accident on the 21 of Dec last year. The damage to my 1995 Honda Civic was fixed, but 2 days later, my radiator pretty much 'sploded and I had to pay an arm and a leg to get THAT fixed, too. Now, I notice my thermostat is nearly going to the red every time I go to work right before the car shifts gears (it's an automatic., and I mostly drive 35-40 mph). Then it will go back to about middle temp/a safe temp before rising again.

I've been told that over heating problems could be due to the radiator (but that's brand new), or the oil (that's brand new, too). Am I missing something?