IgnitionSwitch
The problem could be a mechanical problem it is important to take it to the mechanic to have it checked.
life starts now, September 22 2009,already came out
Since the starter is good but will not turn the engine over when hot, check the engine for free rotation. Turn the engine over by moving the crank by hand (with the ignition off.) The engine could be sticking when hot and not be able to turn over.
normally when a transmission starts to slip there is a problem with one of your sincronizer switches. its just easier when this starts to go to pay someone to rebuild your tranny. im a big gear head and i still get a little shotty working on trannys. trust me get it checked out.
A problem with the fuel system. I'm assuming the fuel pump or carburetor/fuel injectors. I had a 1987 Pontiac Firebird that would sputter for a few seconds when you pressed on the gas pedal. Never got it checked though but I assume that would be the problem.
it starts a little bit after winter has already began
you should probably get it checked out.
Check the Crank Sensor on the Bellhousing!
If the battery light is on, it usually means that the alternator has a problem. Have the alternator checked at a local auto parts retailer. If one or more of the diodes are bad, your battery charge will be affected.
Have you checked the throttle cable?
Money
I have a four wheeler Honda TRX350D Foreman 4x4. Would turn over but not start. Checked oil and it had gas in it. Drained and put in new oil. Checked fuses and tinkered with fuel pump. It now starts and runs but I don't want to use it until I resolve 'oil in gas' problem. Would fuel pump going bad cause the gas/oil problem? Would there be a more reasonable reason for this?