As a Heavy, I have in my posession what is arguably the most powerful close-range weapon in the game. One that can shred through an enemy in fractions of a second.
I am also in posession of the biggest ‘guns’ in the game, them being my massive fists of doom.
Which seems redundant, given the large number of boolits I can shoot with my mighty mighty gun.
So when is it a better idea to spend the time switching to my fists for a good punchfest, over holding out my minigun and preparing for a mowdown?
As with almost every melee weapon, the answer is almost never. This is especially true with the heavy- you have the strongest short range weapon in the game as your primary weapon and you are far too slow to easily punch anyone.
Even if you are out of ammo, punching someone is still a bad idea. A non-critical melee attack usually* deals 65 damage and takes almost a second between attacks. This gives your target plenty of time to back away and shoot you. At this point there is nothing you can do to your target- they’re faster than you.
If you’re looking for a weapon that doesn’t need spinning up, use one of the Heavy’s shotguns.
The real use for your fists is you can swap them for either the Gloves of Running Urgently, which cause you to run faster and take minicrits when wielded or the Fists of Steel, which reduce incoming ranged damage and increase incoming melee damage when wielded.
*Scout, spy and certain unlockable melee weapons change this.