Heihachi is cut from the same cloth as the other samurai in the film, but he's more accepting of it. He smiles a lot more and goes about his work with a sense of cheerfulness. We first find him chopping wood, a task that should be beneath any samurai worth his salt, but that he's taking on with a cheerful air. He even makes a joke about being a student of the "Wood Chop" school of swordsmanship, so he's not at all shy about the dishonor he's suffered. He even points out his own cowardice, suggesting that "it's impossible" to kill all of his enemies, so he runs away instead.
That Zen philosophy makes him a good morale booster for the team, and though he laughingly hints that he might not be up for the job, he happily goes along with it. For that he earns the same reward as three of his other companions: death for the cause and a hero's grave in the villager's cemetery.