Drifter 52:
The first tractor I remember driving was a Farmall H that my father bought on the black market when he returned from the Air Corps at the end of WWII. It had a home made front-end loader (I recall some parts were wood) and I don't recall turning it over or that it was hard to steer, but I was only ten or so years old at the time, so my memory is not the best. Your picture reminds me that the only plastic on those machines were the gearshift knob and steering wheel.
Anyhow, your problem may be a combination of too much heat and too little dissipation. Let me make some assumptions: pump is 8 gpm, lines are 1/2", and the pump body, pump lines, directional control valve, and reservoir hold 4 gallons. At 8gpm the 4g of fluid circulates two times per minute.
The pump appears to be a single section gear pump with a flow divider on the output, which is either a priority flow divider or a proportional divider. One output appears to return to directly to the reservoir. Depending on how the output is directed, the flow divider can cause the pressure drop in the line going from pump to reservoir (tank) to be the same as the pressure drop in the entire flow path for the other pump output stream.
The next part is really guessing (as if the above were not). Say the path through which the other pump output flows consists of 2 10 foot sections of 1/2" hose with fittings and a regular (or mitered) 90 deg elbow on each end, together with a variety of nipples, etc. The flow path also includes the flow divider which almost certainly imposes a significant pressure loss, and the directional control valve which has its own significant pressure losses.
These pressure losses can add up to more than you expect. For example, 10gpm of typical warm (90-100deg f) hydraulic fluid flowing through 10 feet of 1/2" hose with end fittings and an elbow on each end incurs a pressure loss of about 30 psi (that's the only number I can remember from a recent project).
Fors the sake of argument, assume that the accumlated pressure losses in the circuit are 140 psi (I suspect it is more than that). Since the flow divider on the pump probably imposes that same pressure loss on the flow into the reservoir, the full 8gpm incurs a pressure loss of 140 psi.
A rule of thumb (scientifically based) is that the temperature of typical hydraulic fluid increases 1 deg F for every 140 psi of pressure drop that is due to friction (and all these losses are due to friction, not to doing work by moving a piston in a cylinder). So, if you fluid passes through the system twice each minute, the temperature of the fluid increases by 2 deg F per minute.
If your 15 mile trip took an hour (I recall a maximum road speed of roughly that), the hydraulic fluid circulated 120 times and its temperature was raised 120 deg F above ambient temperature. If ambient temperature was 90deg F, the fluid temperature would have increased to 210 deg F.
Of course all that energy from the friction does not remain in the fluid; some passes into the hoses, fittings, pump body, etc. But once those parts heat up the only additional heat they absorb is what they radiate into the surroundings. If those surroundings are also hot, and if the sun is adding more heat to them, they may remove very little heat.
And if any of my assumptions are too low (the pump is 8 gpm rather than 12), the heat increase is much greater (more than just a proportional 150% in this case).
Of course, you could have a fully blocked pump (deadhead), but I doubt it because the heat buildup then would be very fast. If the pressure relief valve is set at 1400 psi, the each time the fluid passes through the system the temperature rises by 10 deg F (1400/140 x 1), which is 20 deg F in this case. It would be boiling in 10-15 minutes in that case.
If it were me, I would remove the flow divider from the pump, combine both pump flows into the working circuit to the control valve rather than send one to the tank, clean up the hoses (new hoses, limit elbows, etc.), and replace the tank with a 10-15 gal one. I think there is a good chance that will solve your problem. If not, you will need the new hoses and tank for the 13 gpm pump anyway. Save the other pump because as long as those old cast iron Farmalls last it will wear out the current pump.
I hope Art is right about the H having 40 horsepower, but I recall it being somewhere around 30. Do you know?
Keep us posted on the project.
Good luck