Alice, be very carefull here, if you have just bought the car, there may be every chance that the head Gasket has gone, did you bye it from a reputable dealer or from the side of the road?
If there is a Mr Alice, get him to check that there is water in the Radiator, the fan belt is tight, the heater motor is working, did you bye the car AS SEEN? was there a warranty with it? If so, take the car back as as possible. If this turns out to be a head Gasket you are talking in the region of £300 to get it sorted, would it be a Peugeot by any chance?
Yes, As Tony regards the Thermostat, You do realise the consequences regards the demister with no heater? you can not demist, your reactions can be effected regards the cold, not given you frighteners Alice, but advice. IF you do take the car back to the garage make sure you DO NOT GET CHARGED for the work, stand your ground.