Over heating

My car over heated today I put more water in it and the thermometer on dash went back to the centre. I did less than half a mile and the thermometer went up to the red again, so I stopped put more water in and the water seemed not to b leaking from anywhere. I have oil in my car so it's not head gasket.
I got home but the thermometer kept jumping up to being near the red again and then went back to the centre.
I called aa and they said possible thermastat or flush out of pipes.
Is this correct Nd how much labour is it.