Overheating ?

Hi i got a Peugeot 307 2005 I only got it recently but it started overheating first time it got to the temperature gauge got to the red danger zone. But since the thermostat was checked and was told it was fine it still heat to 110/120 at times but most times at 90. Is this normal? The fan is kicking in and seems to be doing its job although on the first time it still got to the danger zone. I am worried as to whether will this cause damage to the engine and future problem. Thanks