Thermal Heat Stress on Hydraulic Cylinder

I'd say it depends more on the temperature of the hydraulic fluid.

Pumping adds heat to the fluid. Even bends and obstructions will add heat by making the pump impart more energy into the fluid.

Seals would be the first thing that would succumb to heat.

Either too high or too low of a temperature can damage seals.....

read more....

http://www.parker.com/literature/Literature%20Files/euro_cylinder/v4/Trouble_1242-1-gb.pdf

...and if it expands or contracts too much, leakage and seizure would be things to look out for, as well as burnt paintwork.

Another possibility is operating a cold cylinder in a system where the fluid is hot from already operating other devices. A fluid cooler can alleviate this.

can this phenomenon affect on the piston rod to an extent it change it's color?

Indirectly, maybe. Temperatures over ~250F or 130C can cause oil to darken, which in turn could discolor cylinder rods and barrels. If your temperatures are that high or higher, you need to investigate fluid cooling methods.

This is the problem NASCAR had on the brake systems used on the stock cars on short tracks. At night you can see the rotors glowing almost white hot. That heat is transfered to the calipers, which are nothing more then cylinders. The old design held the same oil in next to the pucks all of the time. Once the heat began to build you would hear everyone begin to say their brakes were fading. Not so much fading as the fluid would turn to steam and as we all know steam or air is compressible.

So the fix was to come up with a caliper that cycled oil through on each pump of the pedal. Thus allowing for cool oil at the puck side all of the time.

This is just one example thats out there, but you can see what can happen when heat is introduce.