My 1995 S-320 blows out cold air and will not heat the cabin. The engine does not over heat. What could be the problem?

Check your flapper doors and blower/ducts for clogs or problems.
Also the cooling system thermostat could be stuck open. Auto heaters have a tiny radiator heater core that uses hot engine coolant to warm the cabin air.
That all has to be working in order to get heat.

the way any motor vehicles interior heater works is by allowing water from the engines cooling system to circulate through a mush smaller radiator located behind the dashboard and the fan blows air through the radiator allowing the warm water to heat the air so when you select warm or cold via the interior controls a valve fitted in line of the water pipes that is linking the engine bay radiator to the interior one allows water to flow which makes me believe that valve is not functioning

The warning lights are probably not related to no heat, unless the engine is low on coolant.
It sounds like a problem with the blend doors under the dash, or the main controller. You may need a shop manual to diagnose it.

Air Temperature Control Blend Door Failure No Heat or no AC (dependes on where door sticks)

In all modern cars there is a tiny DC electric motor driven gear drive that moves a plastic door that blends heated and cooled air from the AC and the heater core, this is called (interestedly enough) the air temperature control blend door actuator. The motor that moves this door fails because the door starts sticking from warping, most common complaint is no heat but it can be no AC as well. To replace these parts (blend door and blend door actuator) you must remove the entire dash from the car. Always have this problem confirmed by a dealer or qualified repair shop as it is a very expensive repair.

Other causes of no heat in the cabin are engine thermostats that are stuck open (engine runs cold) or air bubbles in the cooling system.

Try changing cabin filter in clove box.. mine would barely blow, changed cabin filter for about $14 and work perfect.

porbably your cabin heater (radiator like aparatus inside dash) is clogged with debris. you need to replace it if your blower works but it blows only cold air. but be sure that your engine is warm.

first off all if a/c gas presssure is low or no gas at all ( because of some reason you have already lost it) it acts exactly how you you describe. kicks in and out. but cant cool air inside. (first make dealer check it for leaks and let them fill it with proper yellow flourescent dye added gas)

limited het in cabin heater is another issue. if engine is warm and still not enough heat inside, we can say that you have a clogged cabin heater or air pocket is in hoses connected to cabin heater. you need to bleed cooler radiator inm front. you need to raise infront of car and bleed it with bleeding screw. after this check the heat again if still not enouh heat you may need to replace cabin heater.

if engine is not warm enough when you drive slow or let it idle. this means you have a broken thermostate or it is stuck half open.

the heating core probably went get it checked out... Armando

I think u may have an air temperature control blend door problem, the door is moved by a small electric motor, it is stuck in the cold position.

If you are getting air into the cabin, then there is prbably no abstruction the is keeping the warm air out.

Check the coolant leval. There might be enough to cool the engine, but becuase the heater core is higher than the engine, the coolant might not be able to get to it.