Starts will not stay running only way to keep running is at high rpm,after warmup no problems

no year car told. wow. "I'm having No start fuel problem" why does the first line contradict others?
NO CRANK
cranks good but will not start
cranks good but starts and stalls.
cranks and runs but RPM races to high(too high RPM not told)
normal cold is about 1500 RPM but at -39F RPM will go higher that is how EFI works here. even 2500 is possible say in Alaska.USA.
-80f there. possible (record temp low)
fuel hates to vaporize cold and the colder it is the worse that is
and the PCM knows all that for over 43 years of EFI tech.
is this your first car
or first car cold outside
or first ever Klondyke cold snap?

Any codes?air filter,dirty throttle body.

Check to make sure your battery terminals are tight. You will be amazed how many problems start there. You can also remove both connectors and and clean the terminals very well. Get some dielectric grease from the auto parts store to help prevent oxidation which will also cause problems.

I would look at the cold start injector first and work from there.

ur havin warmup issues--get car scanned--do a complete checover also-makin sure radiator fluid is norml cause the coolant sensor gives info--inspect thermostat-mite not be closed on warmup--throttle body and idle air is probly filthy--

Sounds like a instrument problem. If you remove power at the battery then it should not have power to keep it at the high RPM level. There's nothing there in induce the RPM to range.

what engine would be more helpful. but just guessing i would say the engine is just tired and rings are worn and valves arent seating and you have a vacum causing the high idle from nothing seating properly.

Sounds like a vacumn leak. Gasket under intake plenum may be leaking. Be sure the pcv valve has the o-ring around it in the correct place also as it will set a code.

sounds like either fuel pump weak or fuel filter plugged