Hydrostat? Hot? and black in the oil? Unh-oh... You might have bigger problems than you expect. The heat may be coming from internal bypassing in the drive pumps or drive motors. Heat in hydraulic systems comes from high pressure oil bleeding down into low pressure areas without doing any work. The energy has to go somewhere, and that somewhere is into heating the oil.
The bypassing may be why you are getting heating when you use it for a while and it cools down when stopped and idling. I'll bet that the hydrostat oil cooler is liquid cooled, using engine coolant. So the overheating in the engine coolant makes it look like the engine is the culprit when maybe it really isn't.
To check this out, you need to find a manual to see where to check the case drain flows at each drive pump and each drive motor. The higher the flow, the greater the internal leakage at that item. The manual will tell you what the acceptable flows are--as the pump or motor wears, the flows get higher and can eventually get high enough to overload the cooling system.
Also, the black in the oil is carbonization, which is likely from the internal leakage as well. When the oil squeezes through the internal leakage, it can get super hot, enough to create tiny carbon particles. It seems to me that there are other signs of localized heating that will turn up in an oil sample test result, like the presence of certain gases that show up during localized overheating.
That localized heating can also occur at other places in the drive system-for example, at a faulty pressure relief valve that isn't 100% closed or some of the shuttle valves in the hydrostat system.
I sure hope this isn't your problem--Those hydrostat pumps and motors are kinda pricey and there really isn't a cheap way out of the issue.
Keep us posted on what you find!
Jon.
