2002 Jeep Cherokee Morning sickness

My jeep runs all day perfectly !
The problem is that every morning for the last 3 days when I start the car first it acts like the batterie is low where the engine would turn slowly unlike regulr stat-ups, and if I don't use the accelerator at the same time it won't start, then when it starts for the first five minutes if I release the accelerator pedal it shuts off ! After 5 minutes I can release the pedal but the RPM would start bouncing from 0.3 to 0.6 (normally it used to run steadily on 0.7) up and down while the engine keeps shaking weirdly ! And after 10 or 15 minutes everything else goes back to normal ! Note that the last 3 days we had a sudden drop of temperature in my area I don't know if its any how related ! Could it be the alternator or the fuel pump or what?