My car goes into limp mode when starting if previous journey had been short, however, starts fine if previous journey was long enough for engine to reach normal temp. No warning lights come on and no

first option is to have the fault codes read
limp mode is activated by both the engine and transmission sensors
going to limp mode so quick could be an overheating problem , transmission vss/tcm problem or ECM fault
by reading the fault codes , you will get a better idea of the problem

You 100% need a dealer or a very specialized repair shop.

Limp mode is triggered by a serious issue with the cars transmission or engine controls.

probably not if it is limp mode
the ECM puts the car in limp mode to prevent serious problems in the engine or transmission
could be no coolant, sump oil , transmission oil etc
run the fault codes and find the reason for the mode

Use a bottle of yellow HEET dry gas to remove any moisture problem in the fuel.

Clean / replace air filter.
Check ATF at level ground. Top off ATF to MAX level.

IF THE CRANK SENSER HAS FAILED THE THE CAR WANT START AT ALL.Get a diagnosic check done at your local garage to find the problem.Good luck.

have you spilled any liqueds into the shifter if so it will cause a short in the unit causing it to react like yours.

Replace the temp sensor/switch located on the radiator.  Don't forget to drain your radiator and use teflon tape on the sensor when installing it.  DO NOT over-tighten.

Is the vehicle's Check Engine Light on? It should briefly light up when you turn the key on (before you start the engine) to show that the light is working correctly. Based on what I've read I believe you should have one or more trouble codes. A place like AutoZone will read the trouble codes for you for free, and you can look them up here - http://www.engine-light-help.com/generic-check-engine-light-codes.html

Code 24 is a vehicle speed signal sensor fault, the sensor most likely does not provide a useable signal until about 25 MPH, when the computer doesn't see any signal after that speed it turns on the light. Make sense?