[RPG] How does the secondary effect of the Heat Metal spell interact with a creature resistant/immune to fire damage

RAW there really is only one option to quickly take off armor: have someone help you.

Getting Into and Out of Armor

The time it takes to don or doff armor depends on the armor’s category.

Don. This is the time it takes to put on armor. You benefit from the armor's AC only if you take the full time to don the suit o f armor.

Doff. This is the time it takes to take off armor. If you have help, reduce this time by half.

The fastest a PC could shed heavy armor with help would be in 2 and a half minutes or 25 rounds of combat.

RAW options to avoid the damage

1. Run away. As I interpret the spell you would still need to be in its range to use the bonus action attack. Running out of range would be difficult to achieve since the spell attack is a bonus action allowing the caster to use both their actions to follow you. However if allies impede the movement of the caster or your move speed is greater it could be accomplished in one round.
2. Deal Damage. Every time the magic user takes damage while concentrating on a spell they are forced to make a CON save to keep that spell up. If everyone hits the wizard odds are pretty high that he will fail one of those CON saves.

Houserule option

Let the PC take it off with a standard action, but doing so damages the armor, preventing them from wearing it again until they have it repaired.

Musings on Heat metal

There is no requirement for a PC or NPC whose gear is affected by heat metal to react taking off their armor. The stipulation of the spell is to throw it if they can, donning and doffing seems to be a bit more than all that and as such I would interpret it to mean weapons should be thrown, but armor can be kept on. I know 2d8 bonus action damage sounds like a lot, but dice only damage has a way of only coming out to be around the average most of the time, while 9 damage a round without an attack roll is pretty nice, it is probably a better idea for the party to focus-fire on the wizard to end it rather than someone in heavy armor taking their armor off and seriously lowering their AC for the rest of the fight.

No, it doesn't generally increase the weapon's damage

When you cast Heat Metal on an object you get the following effect, emphasis mine:

Any creature in physical contact with the object takes 2d8 fire damage when you cast the spell. Until the spell ends, you can use a bonus action on each of your subsequent turns to cause this damage again.

Anyone touching the object only actually takes damage from it once immediately when you cast the spell and thereafter when you use a bonus action to cause the damage again. Otherwise, touching the object (despite the heat) does not cause damage, so simply hitting someone with such a metal object wouldn't do any more damage than normal - you don't have to worry about accidentally giving your foes a boost by using the spell against them.

Action shenanigans!

The above said, there are a couple of ways I would allow you to get this kind of effect if you were deliberately trying to.

Firstly, if you readied the spell to be cast at the moment the target object was used to hit someone, I'd rule that both the wielder and their target were both in contact with the object at the time of casting, so both would take the damage.

Secondly, if you were to cast it on a weapon you were holding yourself, then on subsequent turns you could in principle use your bonus action to cause the extra damage exactly when you hit someone with it (since a bonus action without timing specified can be used whenever you like on your turn). That would get you one hit per round with some extra damage.

Obviously not a recommended strategy for use on yourself/friends unless you've got fire resistance or immunity.