I'd be tempted to replace the sensor(s) first. If the computer is getting wrong information it'll do strange things. There are two coolant temperature sensors. One is at the front of the head by the thermostat housing. The other is a fun one on the back of the head. However, it's not necessary to replace both just to see if they're the problem. You can unplug both sensors and plug the wires into the new ones. If the car starts and runs normally, you know what your issue is and can then go about replacing them. Expect to spend about $70 or $80 on new sensors. The one at the back of the head is the one that provides the information for the computer as far as my experience goes. I replaced the front one first and it did nothing to fix the problem. Replacing the rear one cured it.

It might be a good idea to get the codes read to see what the computer thinks the problem is as well...

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Dale