I have a 96 Accord LX four cylinders.

Every time I start my car in the morning I hear water running through the whole engine when I accelerate. Today after coming from college I passed by to a Jack in the Box and I noticed that my temperature raised from 40% to 65% so I turned it off and later after I turned it back on the temperature was the same but I accelarated and the temperature went back to normal, I opened the hood and no burning smell came out and I even accelarated the engine hard to see if the temperature raised again but it didn't.
Can anyone help me is it the thermostat or my radiator. The engine is new it has less 100,000 miles and the radiator seems semi-used so what's wrong? thanks