Can anyone explain what the temperature probe has to do with the starter engine? I can't see the relationship and it is not a pussy.
If you take away the temperature probe with the hot engine (or cold it does not matter) you will have a fault code immediately in the switchboard, however, go to pass as a dosage for cold engine, (rich mixture) with what it is possible that you start better.
But what I can't understand is that if the starter engine turns very cold or hot, why change it ???.
My opinion, which does not have to be the correct one is:
1st spark plugs, possibly too spent, spark excessively long and therefore poor, difficulty igniting gasoline.
2nd If you have electronic accelerator (it does not have accelerator cable in the gas butterfly) it is easy for the oil and the shit that are stuck to the butterfly prevent the entrance of enough air into the collector. If this is so, a rating will be noticed, unstable slowed and tendency to stand when after reducing marches (from third to second and we step on clutch and brake to stop at a traffic light) it is covered or is about to do so.
The solution is easy:
1º Remove the spark plugs and see if they are well
2nd to disassemble and clean the butterfly body and the butterfly of gas with gasoline or diesel and dry with compressed air or a cloth that does not leave threads.
All the best.