The most common problem is the rubber sealing strip that runs along the top of the firewall, touching the underside of the bonnet. This stops hot air from the engine bay getting into the ventilation system. If that rubber is hardened or flattened or missing or broken or if the bonnet is sitting too high then you'll always have hot air in the vents. Given the age of NAs now there's probably not an NA in the world that hasn't had this problem. The easiest solution is to buy a new sealing strip from Mazda. They used to be about $40 and take 1 minute to fit. Otherwise there's a whole range of dodgy fixes mentioned elsewhere on this forum and on miata.net. Just google for things like hot air in the vents. As far as I know none of the dodgy fixes last long.
Occasionally there's a problem with adjustment or breakage of the linkage between the hot/cold air control and its flap. Work your hand in behind the centre console near the clutch pedal and feel for it as you move the hot/cold lever back and forth. When you find it then you'll know which covers you need to remove to get to it. Make sure it's properly connected. With the covers off you'll also be able to see that you can adjust the settings to bias it more towards hot or cold, depending what your problem was.
I'd check the and fix the sealing strip first. 90% of heat and bad A/C problems stem from that.
