Not to pick on you, but I’ll take this opportunity to advise all reading here that when you take your car (or any device or even your body) in for fixing, describe the symptoms you observe without trying to diagnose it. First we’re told it’s overheating, then smoking, then that the temp gauge indicates it’s NOT overheating. If you see smoke, say so, and feel free to mention that you suspect it might be overheating. But don’t say it IS overheating just because you think it MIGHT be. [/sermon]
It would be helpful to know if it’s smoke or steam you’re seeing. If it’s smoke, it could be from oil leakage onto part of the exhaust, a belt slipping, or in this case possibly an air conditioning clutch slipping. If it’s steam, it’s pretty well gotta be a cooling system (antifreeze) leak.
It is possible that’s it’s overheating and that the temp gauge is incorrect. This can be determined by measuring the cooling system temperature. If it’s been driven a fair amount with this symptom and has not lost antifreeze, it’s unlikely it’s overheating.
Your mention of it going faster with the A/C on implies a problem with the A/C belt and/or clutch, leakage of A/C oil onto something hot, or cooling system leakage (the A/C system puts extra heat load onto the engine, stressing the cooling system).
The REC means “recirculate”–in this position it recirculates the car’s inside air rather than drawing in fresh outside air. Use this position only for coldest A/C after it has started cooling–do not use this for heat, defrost, or vent; or for A/C when the inside of the car is hot (like after parked in the sun). Why that button is flashing, I don’t know, but some Japanese cars flash a button (usually one labeled “A/C”) when there’s a problem with the A/C clutch.
First suggestion, check the engine coolant (antifreeze) level in the radiator–ONLY WITH THE ENGINE COLD. Do not rely on the overflow jar for this. If it’s up to the brim in the radiator, you haven’t lost coolant, which should eliminate steam and overheating from consideration. If it’s noticeably low, it’s wisest to not drive the car as it might be overheating, and severe overheating can cause engine damage.
Second suggestion, check the belts, especially the A/C belt. A too-loose belt could slip and smoke, as could a belt fighting a pulley that won’t turn properly.