Car keeps running hot but the radiator isnt hot . when u touch the cap it is not hot.

take of cap run the car till its hot should start to over flow. another method make sure both radiator hoses are warm or hot to the touch. Should be able to sence flow once the thermostat opens up.

Remove thermostat and test it by dipping it in cold water ib an open pot. Heat the water on the stove while observing the thermostat. It shold opel just before the water boils. If it does check the radiator itself for clogging. Also fluch the engine water galleries.

buy a brand new radiator cap

yes, but it's designed to drive the air out as long as you open the cap and run it until it's hot, keeping the radiator full. Eventually the air will come out and heater hoses should get coolant.

the rad cap is on the overflow tank

First make sure your cooling fans are working properly. As far as the coolant having to be added there has to be either a leak externally or internally on the engine unless your letting it get hot enough to boil over into the reservoir tank. One way to find a leak quickly is to do a pressure test of the coolant system. You will need a special tool to do this. It attaches to the radiator filler neck and you use a small hand pump to pressurize the coolant system to the rated psi on the radiator cap. If you don't have the tool you may be able to rent it from an auto parts store that has a loan-a-tool program. If not a repair shop can do it for you. Once you start to pressurize the system if it's leaking externally you should see it or hear it or both. If you don't then your leak may be internal meaning a possible head gasket leak. Even though your car is running fine a small head gasket leak can cause it to run hotter than normal and loose coolant. Also don't rule out the other items in your coolant system if you find no leaks like your thermostat, water pump or something as simple as a good coolant system flush may be all you need. One note, if you do the pressure test your self and your system will not hold pressure but you find no external leaks, that's another indication of a possible head gasket leak. Once you pressurize with the tool a good coolant sytem it should maintain pressure and not bleed off. Hope that helps, gl.

you need to verify and fill the coolant in the radiator and reserve when the engine is cold,also check to make sure your cooling fans are kicking on when it is hot

have u replaced the radiator and hoses? Thermostat could also be stuck open. Water pump could also be your issue. with motor cool and of remove radiator cap(cap may be bad as well) top-off fluid and start car check for fluid flow with flashlight. Water pumps typically leak from what is called a weep hole when the shaft seal fails. Yours will be located under the timing cover (drivers side) running of the timing belt.
Hit me up after u have check on these.

under maximium load your cooling system is struggling asuming you have an automatic transmission,it is cooled through the radiator,when running the ac your condenser is hot,right in front of the radiator,if your not leaking,and your anti-freeze looks bright green an clean ,and the fan or fans are working ,first change the thermostat,cheapest,remove the serpintine belt and inspect the water pump pulley,spin it by hand,try to tip it forward and backward,to see if it wobbles,it should spin smooth and quiet,if it has a chattering or growling feel,or the pulley wobbles change the pump,the only thing left is the radiator ,make sure that debri or something isnt stuck in front of it a small piece of paper is enough to restrict airflow,inspect the core is it turning green and the fins are falling out ,is the plastic shroud intact around it, lots of things could be going on ,the transmission could be low on fluid,and running hot,causing the excessive load on the radiator,disregaurd this if you have a manual.need more info to pinpoint further,hope this helps