That's pretty instantaneous. If you are just sitting there idling, does the temp gradually rise? I've never know the needle to rise so quickly like that with the gas pedal. The coolant is topped up, yes? When you get off the gas, does the needle immediately go back down?
If everything looks okay, the only thing I can think of are these two things:
- The thermostat is stuck closed, not allowing coolant to circulate through the engine. So you keep heating up the cooleant in the engine. But I would expect there to be something of a delay between stepping on the gas pedal and the needle going up/down
- As weird as it might sound, if the needle stays exactly with your gas pedal, then I think there's an electrical issue - and the needle is following your RPMs and not the gas pedal. If you the car in neutral, and step on the gas pedal, does the needle go up like what you have been describing?