It makes a difference because the drive mechanisms and rods, if the item is a steamer, are not precision-bearing surfaces. When you reverse a drive-train in our scale models, different thrust vectors cause 'bunching', or slack to take place at various places which causes shaped geometries, or engineered surfaces, to alter their angles of interface and the friction that results. That changes the running characteristics. By running the item in both direction, you learn which way the drive train bucks or grabs, and you learn if you have to place spacers between the pillow block/transmission and the worm gear on the main shaft. Most of us learn that an engine that runs well in reverse does not necessarily run well moving forward. Breaking in a locomotive in both directions helps to settle the drivetrain in. Once the drive has some wear, faults that cause stumbling or lurching, but only in one direction, can be investigated and cured. Even so, a break-in after the cure might also be necessary.
And yes, cooling is important. When things cool, especially items that were running in tight tolerances because of friction, their shapes change, both in cross-section and in length. Allowing periodic cooling allows abraded materials to be drawn to one side, or shoved out of the way the next time the sliding/moving/rotating item is set in motion. This has the happy outcome of ridding the friction surfaces of unnecessary wear.