Why won't my car heater work?

It could be a switch/electrical issue; but it could also be something much more such as a busted heater core which is heated by engine coolant liquid. Do you smell anything like antifreeze or fishy?

Fiestas have a frequent problem with the heater control valve, which looks like this. It’s located at the back of the engine compartment, at around the top center of this picture. Not an expensive part; around 40 quid.

edit: Sorry, that 2nd link should have gone here

I think @thorninmud hit the nail on the head.
Also just lift the radiator cap and make sure there are no signs of rust in the coolant, if so your cooling system may be blocked and need flushed.

Assuming that the cooling system is otherwise functional (the engine isn’t overheating) then either you are over-cooling (my Corolla does this), your heater core is clogged, or the control valve is screwy (again, my Corolla does this; after 26 years, it’s a little wonky). However, I am inclined to go with @thorninmud on this one.

I’m going to have to agree with @thorninmud & @jerv here. Although I have a decent troubleshooting method for heater cores, because many of them are a PAIN IN THE A$$ to replace; unless of course you don’t care if you pay out the bum for someone else to repair it. Turn on the car and let it warm up to operating temperature. When up to temp, if you know where the core is, see if any warmth whatsoever is coming from that area. If not, this means there’s no coolant flowing through it. Another way to test this theory is to find the two hoses that are going to the core. Often found going through the passenger side of the firewall. Figure out which is the return line and pull it off while the engine is running, if coolant doesn’t spew out of the hose (like it should) than you have a problem. Next pull off the intake line, (the line that feeds the core with coolant) and see if it’s flowing through there. Which most likely it is. The second test is to make sure it’s the core and not blockage in the line before the core.

lol – might want to check the coolant level first. I was driving a taxi last winter and, in thinking of the other possible mechanical issues, froze my butt off for days. . . when. . . it was just. . . the antifreeze. Granted, a low antifreeze level is a warning of leakage or, otherwise, evaporation of fluid but in the short term . . .