Sounds like a bad bypass valve in the hydrostat. Nothing major if it is that. When the oil cold it is thicker, less viscous, and is not leaking by the bypass as much. Once the oil is hot, it flows easier thru small gaps.
If you still have normal motion in forward, it is not going to be a major rebuild or new pump. The bypass is located on the hydro pump, there should be two, one for forward and one for reverse. A repair manual would tell you exactly which one. Bypass valves should be anywhere from $20 to about $75, depending on pump size and manufacture.
If you find broken parts/pieces in the bypass valve, try to account for all parts and/or pieces. Even a small piece of metal floating around in a hydro system can cost big $$$s.
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