It sounds like it might be the switch or an overheated connector. Finding it might be difficult.
If a 2000 Grand Am sometimes has the heater blower working and sometimes it won't, the problem could be with the heater relay switch. The heater relay switch lets the heater blower know when to come on and when to go off. In most vehicles this switch is behind the glove compartment. This part sometimes gets corroded from condensation in this area.
could be a fuse, a relay, the blower motor or the blower resistor. It's easy to check the fuse, using the owners manual. I am not sure where the relay is, and it requires special tools or replacement with a known good relay to test. If the blower works on high and no other speed, then the resistor is bad. If fuse and relay are good, and blower does not work in any position, suspect the blower motor itself.
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