Charge up your battery. Gone are the days when you could tell it was fully charge by verifying that it was up to a specific gravity of 1.265. So, charge up your battery for at least 24 hrs.
Put your trusty ol’ volt meter across the battery terminals and push the START button, observe voltage. > 9.5 volts, sweet (else not so sweet and battery is suspect).
Place volt meter + lead (red) on the Batt + terminal, place the volt meter – (black) lead on the POSITIVE terminal of the starter MOTOR. Push the start button. The value you read is the voltage drop across the positive power cable. Record this voltage.
Place volt meter + lead (red) on the Batt – terminal, place the volt meter – lead (black) on the engine block. Push the start button. The value you read is the voltage drop across the negative power cable. Record this voltage.
Add the voltage drop of the positive cable to the negative cable. This is the total voltage loss from the cables while the starter is turning. Subtract the total cable loss from the battery voltage while cranking. The resulting number is the actual voltage being supplied to the starter.
(Short cut all this BS and put the volt meter red lead on the starter motor PLUS terminal and the black lead on the engine block. With your third hand press the starter button and read the meter. This is the actual starter motor voltage, if it is low, do the cable drop test to determine if it is the cables or the battery.)
The ignition coils need at least 8.5 volts or more to be able to generate a spark hot enough to initiate combustion. Typically, a range of 9.0 to 9.5 volts at the coils is best. Even though the engine turns over, the voltage to the coils must meet this minimum voltage or it ain’t gonna start. The voltage at the coils is switched ignition voltage, lower than battery voltage; measure directly at the PLUS terminal of one of the coils.
Heavy (excessive) voltage drop during cranking will cause the electronics to ‘zero out’. With a charged voltage of = or > than 12.8 volts your battery should be as fully charged as possible. Heat has a negative effect (loss of efficiency) on both the starter motor as well as the cables; but heat benefits the battery. Cold improves the starting circuit efficiency, but degrades battery performance. Since you cold start OK, but not hot, you may want to perform the above tests.