Vehicle vibrates a little when at a stop and starts to overheat , once I get going the temperature starts dropping back to middle. What do you think the problem is?
Does it actually overheat, or does it just go very near the red portion of the meter, with a sound of the radiator fan running?
If the latter, it's perfectly normal. I have had every single car with no start/stop that I owned do the same.
As there's no airflow at standstill, the radiator fan is needed. Its starting point is purposefully larger than the point where the thermostat kicks in.
So, if you normally see your temperature at 90 degrees, and at standstill they climb to 100 degrees and then the radiator fan kicks in, but the red portion starts only from 110 degrees, don't worry. Your car is working just as designed.
Edit: in a perfectly functional system, the fan kick-in temperature is what determines the max temperature the car should encounter. So, if the temperatures climb significantly even AFTER the fan has kicked in, you might want to get your cooling system checked. In a fully working system, the temperature might rise very slightly after the fan kicks in, but then the temperature will soon become lower, perhaps even so low that the fan stops spinning, until the temperatures rise and the fan kicks in again.
And oh, if you don't know whether the fan is on, it is off. The fan is loud! Trust me, you will hear it.