Diesel Engine Misfire: Why It Happens & Fixes

Hello,
I have a 20-year-old John Deere lawn tractor with a 3-cylinder diesel engine that has always been very reliable.
"When it's cold, everything runs perfectly. But after about 10 minutes of running, it starts to jerk and sputter badly. If it sits for 5 minutes, it goes back to normal, but then after another 5 minutes, it starts doing the same thing again."
Diesel filter replaced, air filter checked. Fuel tank, etc. checked, everything is okay.
Are those the fuel injectors?
Or is it the diesel pump, or the control unit, or a sensor?
Does anyone have a suggestion?

Regards,

Ralf.

"The fuel line might be slightly leaking and drawing in air. This can happen if some of the hose clamps aren't as tight as they used to be and are coming loose. We experienced something similar with a lawn tractor (with a two-cylinder diesel engine). We searched for years, and we eventually found the problem almost by chance while replacing the glow plugs."