My A/C in my 2001 Mazda Protege blows less cool air when I am not moving or moving slower.

SOURCE: 2004 Mazda RX8 Heater problem

There is a well known problem that is a manufacturer's defect with the soldered connection on the circuit board behind the temperature knob. There is a fix to re-solder the connections but the dealer will gladly take $450 to replace it with the same bad board that will last you a while. Look for the link to show you how to fix it yourself.

SOURCE: 1995 mazda protege having problems running during aceleration

change the transmission fluid, replace the oil and oil filter check spark plug cables, check starter coilpak, and make sure there is coolant

SOURCE: 2001 mazda protege keeps stalling

my 2001 mazda protege starts hard, idles low and high at various times (never normal) and it acts as though its going to stall at all times. sparks and wires are changed no help, changed air filter no help. any idea on what to do?

SOURCE: For 2003 Mazda Protege ES model 2.0L 4cyl engine;

Check the air inlet boot going from the air filter to the intake for rips or holes. If rips exist, this would allow air to bypass the filter and mass air flow sensor and will lead to a check engine light appearing. The code would read "too lean, bank 1." If this problem is allowed to continue for long periods of time, the EGR ports will have to be cleaned out and maybe even the intake.

SOURCE: 2001 Mazda Protege cooling fan or thermostat

I am realizing that the cooling fan in this car is very important. It has two in case you didn't notice. The driver side fan motor is bad in mine and the only result is poor air conditioner performance in stop and go traffic. It's fine at high speeds. I would think the thermostat is likely the culprit in your case, but if the fans are not working at all, you should get those replaced. The motors may be bad in both, which could definitely cause overheating. I've been researching prices and you should be able to get the parts for less than $100 each and installation is just a couple of bolts on each assembly.