When was the last time you changed the hydraulic fluid, filter and cleaned the pickup screen. Since it only happens when things are hot, I wonder if the hydraulic fluid is thinning some and getting pass the o-rings or inlet check valve in the brake value. The following is for the 5X10, but I think it would be the same for the 5x20.
When either brake pedal is pressed, the brake piston is moved to the front, thereby closing inlet check valve, which immediately closes brake valve reservoir. As it travel further, the piston opens pressure equalizing valve, trapping the oil in equalizing passage. The increase in pressure causes outlet check valve to open and the oil is forced under pressure to either brake housing. When both brake pedals are pressed, pressure oil flows through both outlet check valves to the brake housings causing the pistons to open both pressure equalizing valves, and the pressure in both brake cylinders is equalized. The outlet check valves ensure a simultaneous braking effect. The pressure equalizing valves and outlet check valves ensure equal braking.
JDparts
John Deere - Parts Catalog
5X20 operator manual
http://manuals.deere.com/omview/OMRE199128_19/?tM=FR
When either brake pedal is pressed, the brake piston is moved to the front, thereby closing inlet check valve, which immediately closes brake valve reservoir. As it travel further, the piston opens pressure equalizing valve, trapping the oil in equalizing passage. The increase in pressure causes outlet check valve to open and the oil is forced under pressure to either brake housing. When both brake pedals are pressed, pressure oil flows through both outlet check valves to the brake housings causing the pistons to open both pressure equalizing valves, and the pressure in both brake cylinders is equalized. The outlet check valves ensure a simultaneous braking effect. The pressure equalizing valves and outlet check valves ensure equal braking.
JDparts
John Deere - Parts Catalog
5X20 operator manual
http://manuals.deere.com/omview/OMRE199128_19/?tM=FR