I have a 2008 mazda 3 with a 2.3L engine. Problem I have is the ac is blowing hot air. Had the ac system checked for leaks and none found and recharged. Ran cold for a week then started blowing hot air. AC compressor works and the condenser fan works. Both come on when the ac is turned on. I have suspension that evaporator is clogged and not allowing the freon to flow. The evaporator lines in the engine compartment aren't either hot or cold indicating freon is flowing. Checked the heat and ac control panel everything is working well

 

I am having the same problem with my '04 mazda 3. It has the same specs as yours. I have had mine checked out by two trusted mechanics. And they both think it is the compressor. My compressor makes a noticeable noice when im driving and i can hear it cut on and off. You might want to take a look at yours.

 

I have both of your solutions, are you ready?

When was the last time you replaced your cabin air filter? If your response is "what cabin air filter?" then I got your problem.

If the cabin air filter is clogged, it rests directly on the AC condenser. It will prevent the air from flowing across the coils and cooling down. It needs to be clean and free flowing.

I had the EXACT same problem as you and I changed the filter (it was black) and pulled out a ton of clogged leaves and gunk and now the AC blows cold as ever.

Do a youtube search for the method to do it. I used the method where you do not remove the glovebox, it took me about 30 minutes and a bunch of swearing.

Enjoy!
RGAZ