I'm trying to solve the same kind of a problem for a 96 Protege which, in addition to stalling out, is also overheating.
Assuming the same kind of symptoms are involved in your case, and also assuming that
(1) your engine's water/coolant levels are up to standards and
(2) the engine's not leaking water/coolant anywhere,
(3) there are no compression or ignition-related issues such as shot rings or bad spark plugs
the most likely culprit here is apparently the thermostat.
Find the WikiAnswers article that addresses that issue.
To test the thermostat, remove it from the engine and place it in water that's been brought somewhere close to a boil. If the thermostat [valve] opens up, it's still good. In this case, buy a new gasket and reinstall the thermostat or, since they're not that expensive, just go ahead and pick up a new one and stash the old one as an emergency backup. The main goal here is diagnostic. If the thermostat opened up just fine, well, the problem's somewhere else.
If the problem's somewhere else, it's still most likely related directly to the cooling system. I don't yet know this engine well enough to go into great detail. But a pretty standard problem is a failed water pump. These can be a pain to replace but are well within the means of the typical owner to handle and shouldn't be more than half a bill total. There'll probably be a "core charge", though, unless you give them the old water pump when you purchase the new one. It's also smart to add a light, even smear of Form-A-Gasket to both sides of the stock, paper gasket that comes with the pump. The easiest way to do this is to attach it to the water pump before installing it and, of course, give it time to dry so that it can't move out of position when you go to bolt it on. Also make sure that the old gasket is cleanly removed from the engine block.
If the car's stalling but not overheating, the problem is one of either fuel flow or air flow.
? FUEL FLOW
If it's a fuel flow problem, it's probably not the fuel filter because, well, a clogged fuel filter causes problems under all operating conditions, not just idle or low rpm. Same goes for the fuel pump. So here, what's likely at issue is carbon build-up, (deposits), at the fuel injectors. Try a bottle of Chevron Techron concentrate and see if over, say, a week it breaks that stuff down. Don't use STP, Gumout, etc. Lucas is also reported to cause problems. Go with the good stuff, and follow the directions to a tee. Also, in the future use only top tier gasoline and avoid premium grade when regular does just fine. Premium gas burns more slowly [than regular] and increases the likelhood of deposition. Top tier fuels contain detergents, (additional petroleum distillates), designed to discourage deposition. Shell, Chevron and Texaco are best bets.
If the problem persists, it may be an air flow problem but, more likely, just means that a professional grade cleaning is needed. Ask around to see which local garage has a good reputation for this kind of work. But it'll cost a couple of bills. If the problem still persists, air flow is at issue and will call for replacing one or more engine components. It's tough to spend this kind of money and still have a problem, but the professional cleaning will pay its own dividend down the road once the real problem has been identified and resolved. I think the phrase is "Zoom, Zoom, Zoom".
? AIR FLOW
If it's an air flow problem, it's probably not the air filter because, as mentioned for the fuel filter, problems would show up under all operating conditions rather than only some. Here, then, what may be at issue is either a sensor or a mechanical device. The sensor keeps track of airflow and reports that information back to the computer. The computer then uses that information to control a mechanical device, usually a small motor that constantly regulates the amount of air that gets mixed in with the fuel.
The sensor is either a "mass airflow meter" or a "manifold absolute pressure meter". (I don't know which for this engine). Regardless, they both serve the same role.
The mechanical device is an "idle air controller" and is bound to be mounted somewhere close to the throttle assembly, that is, the part that's moved by a cable when you press the fuel pedal.
Hopefully it doesn't come to this but, since the idle air controller is usually easier to identify and/or get to, I'd start by replacing it. If problems persist, a sensor is at issue. And though there are probably one or more sensors geared toward regulating emissions and which, for their role, can have an impact on idle conditions, it's more likely one of the sensors I mentioned that's the problem. Finding them, however, may call for professional know-how.
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