It is not specified wether that heat does or doesn't affect an attacker who strikes the heated creature with a natural weapon or unarmed strike, or who is grappling or grappled.
On one hand, one could say yes because the creature is burning-hot and that's just it.
On the other hand, one could say that the heat is harmless for the contact of just a fleeting moment as attacks generally do, because the heat of the creature transfers to its metallic weapons after a given time they're in contact with it. This, though, would invalidate the fact that the creature's mere touch too deals fire damage, and grappling would remain an open question.
Should I simply assume that yes, a natural weapon/unarmed strike attacker and a grappling or grappled creature do take the damage?
This should also modify Efreet, Salamander and whatever other creature had Heat in the first Bestiary.
Should I simply assume that yes, a natural weapon/unarmed strike attacker and a grappling or grappled creature do take the damage?
Nope. You can house rule it that way, of course but it would change dynamics of fighting creatures that were given heat ability by developers in the first place. If it was to deal damage to attackers it would be stated so.
If you want in-game explanation - think of it that the heat is distributed on the creature or around the creature and only focuses to deal actual damage when the creature actively attacks. Or even that heat only activates in sudden surge of temperature during attacks.
it would change dynamics of fighting creatures that were given heat ability by developers in the first place
While that's obviously true, I can hardly imagine that they didn't say anything about grappling and striking creatures due to a highly imaginative explanation they came up in their minds without providing it to readers. In the sphere of probability, I'm far more prone to think that they forgot to explain something; wouldn't be the first time and surely won't be the last one.