We just recently picked up a D19 and found it to have a few problems we need to troubleshoot. 

The problem we are trying to track down right now is that it starts and runs fine until it warms up and we start doing work with it. After a while(about 20 minutes) it starts to have trouble maintaining RPM and shuts down. It is very hard to get running again until it cools for a while. Once I get it running it will go for a much shorter time before it has problems again. 

We suspected coolant level but that was fine, our next step this weekend to check if he water pump has failed. The water temp gauge doesn't work but that might be just a busted gauge, this tractor has not been well maintained.  Any ideas from the experts on the forum?

I found a plate on the engine block that looks like it my be a S/N but it doesn't match at all with the serial numbers in my operators manual. 

I found- 

G-262(I'm assuming this is cubic inches since it is 262ci)

G-50797

4515925

That's an engine serial #, the tractor number should be about an inch to the rear of it. On the bell housing.

When it starts running bad, after 20 minutes or so, I would suspect a bad ignition coil.  Check the spark...

It has OEM wiring on it still which is brittle and cracking, I have been concerned about a short somewhere on the tractor. 

  

  I fought with a D17 that would run about that long and burn points and made you think that it was a gas issue, and clean the carb and file the points over and over, put new ignition parts in 3 times. It made you think you don't know how to fix the problem... I finally figured out that the two previous owners had gotten rid of the tractor for the same reason.   I realized it was burning the points, so I put a GM car resistor in and it ran alllll day working it. Later updated it to the wiring of a later series D17.  It starts anytime now. 

 Hope it is that simple for you.

It seems that this is getting better by moment. Here is what we discovered today.

The battery is grounded on the negative side. However it appears that the original generator is still installed. And it appears that that coil that we blew was wired backwards. Meaning, the feed that comes from the ignition switch is attached to the positive side of the coil.  

It "looks" like some one tried to convert this tractor to negative ground. Is that even possible while keeping the original generator installed?

I'll post a pic of the generator, or at least what I assume is the generator. I dunno if they make alternators that look like generators or not, but it sure looks like an old generator. 

I see some "how to guides" recommending I remove the belt and have the tractor running when I polarize the generator. Is that necessary? 

You should be using a 12 v coil, with NO EXTERNAL resistor. With negative ground, the wire from the switch would be POSITIVE and go to the POSITIVE terminal on the coil.. NEG terminal goes to the point.

 There was a reason when Allis went from the resistor coil to the 4 post Solenoid and then feed full 12 volts to the coil on start up, and they changed the coil too. 

  I know our old D17 needed a battery charger on the battery if we started it to clean barnat -30, and that was with a new battery... but we usually plugged in the tank heater when it was getting around zero for easier starts.  That tractor was the three post solenoid. 

  In the same below zero temperatures, the 170 would start because it had full voltage to coil despite the heavier draw on the battery to turn the hydraulic pump too.

    My uncle had a story of very near same problem back in the days when they had a cheap model of the Plymouth car, if it got down to 10 below, that car would refuse to start. He wondered why, and found that to make that Plymouth, they simply did not equip that car with full voltage on start up. He put on what would supply the full voltage and said it didn't matter after that what kind of weather they had, it started and went.  That is the importance of having enough spark at the plugs when you need it. A poor spark don't cut it when it gets dam cold... Now they have hotter coils than what we had back then so... maybe you don't need full voltage now.   In my opinion and experience, that four post was needed and of a good design to get the job done.

  We had a 1954 Plymouth Belveder that could sit in the snow bank and when needed, just jump in and turn the key and it would start... while the dam ford falcon 4d sat in the garage and take a half hour of cranking before it thought about starting... And I will bet that it was lacking hot spark on the cold days... and that thing was the damdest cold car we ever road in. The plymouth and the dodge had far more comfort.

A 6 volt coil should have 1.5 OHMS inside... a 12 volt coil should have 3.0 OHMS inside... since volts is OHMS x  amps... they should both draw the same amps.