When it is cold outside, the foot accelerator is stiff and when we start it the engine races “wide open”, like it is floored. I turn the car off, get under the hood, and push on a set screw type mechanism near the CFI. The car will start but the pedal is still stiff. Driving slowly, pressing the accelerator, the engine still idles fast. Then after about ten minutes of driving it seems to be ok.
My guess is the cable from the gas pedal through the firewall and up to the CFI needs lubrication. The linkage could use lubricating also. There are areosol lubricants made for motorcycle cables that should work for you.
A sticky gas petal is dangerous so you need to deal with this now, or take it to your favorite mechanic. It does not sound complicated to fix.
If not already done, clean the throttle body with throttle body cleaner. If there’s a buildup of gum and varnish in the throttle body, this can become stiff in cold weather. This can cause the accelerator to be stiff to apply, and then cause the throttle plate to hang open. Once the engine gets hot enough, the gum and varnish softens up where the accelerator functions normally and throttle plate doesn’t hang open.
You could have carburetor icing. Is there water in the air cleaner? There could be coolant in the oil due to head gasket leaking or a bad water pump gasket or unsealed bolt. The crankcase vent lets steam get to the air cleaner when the engine is shut off. The throttle freezing stops when the engine is warm.
Another version of the problem is when a choke gets frozen in the open position. The car won’t start until the driver forces the ckoke to close.
Also check the throttle position sensor–if this sensor is bad the computer can’t determine how far the throttle is open and your engine will either rev too high or have lousy throttle response (or both)