Your heater, like most cars, works from the heater core. It sounds like your thermostat is opening up if you can get air for a minute, but it goes back off. The thermostat may be closing again, or there me be a blockage in the heater core.
If you're wanting to try replacing parts, I would start with the thermostat first. They're usually pretty cheap, and most people can even put them in themselves. Heater cores, on the other hand, can be a pain to deal with. Most of them are under the dash, and can only be taken out by taking parts of the dash out.
Also, what's the temperatures like there? Has antifreeze been put into the car? List more symptoms and details in your question if you can think of any.