It's almost certainly the thermal fuse blown, it lives in the airflow of the heating duct behind the dash. On my car it's accessible by removing the glovebox and delving in the innards. This was by far the most trying part of the job, once cracked the rest is straightforward. Some cars have a credit-card shaped encapsulated resistor pack ... these are not fixable by the following method.
To avoid history repeating itself do check that you have not got any leaves or other crud partially blocking the airflow through the heater. The air intake is usually at the foot of the windscreen by the wipers, you'll have to remove a screening grille to get at it. Reduced airflow causes the system to run hot and the thermal fuse to blow.
I'm currently glowing with satisfaction at having just solved just this problem on my P reg Laguna RT estate saving myself 99% of the quoted spare part price by buying a 128C thermal fuse from Maplin for 69p!
If your is like mine, get behind the dash / through the glovebox opening and disconnect the multi-way plugs connecting the resistor pack to the heating duct and the blower motor. Once you’ve got it out you should see several little coils (like tiny electric fire elements) under a shield... carefully remove the shield. Under the coils runs a component that looks like a resistor or diode but is actually a thermal fuse ... it melts if it gets too hot. If you have a meter, check to see if it has blown. Mine had.
Cut it out, clean it up and get a magnifier on it to try to read the temperature rating. Mine was 121C ... the closest Maplin had was 128C = good enough.
IMPORTANT: If soldering the replacement into place remember that it's designed to melt when it gets hot. Soldering irons work at about 200C so you'll need a HEAT SINK between the iron and the capsule of the fuse to avoid melting it. I used a pair of long nosed pliers with a rubber hand around the handles to keep them on the job.
But ... it's worked a treat for me, I’m so chuffed!!
Good Luck.
Mike Rochester
October 2009