there's no special code generated by the ECU to not enable a start below 40 deg F , so there is something wrong
just to clarify that you say its not cranking?
so the motor isn't actually turning over on the starter at all? if this is the case then check that the main battery cables are on tight and the terminals are clean and bright. Do the same for the engine / gearbox earth strap.
Then follow the main positive lead back to the engine and down to the starter motor, and check the connection at this end as well.
There should also be a small wire to the motor which should have 12V when you're turning the ignition switch to crank. If the 12V isn't there, check back along this wire for damage to the insulation or corroded connections
This 12V feed comes directly from the ignition switch so this may be faulty and need replacing
Check the resistance of the main positive lead that runs down to the motor as anything more than a few ohms and it should be replaced
Don't forget to try a jump start from another car / battery as its possible the battery is poor, if you have a voltmeter a healthy battery should read 12.7+V
also try substituting the battery for another as I've known a very flat battery to drag down the system voltage too far even with jump cables
one other thing to consider is that the immobiliser is faulty and preventing the starter from being enabled - however if the dash / ignition lights are on then this usually means that its off
If this is all OK then its possible the car needs a new starter motor