Page 146 of the PHB has the table for getting in and out of armour (1 to 5 minutes to doff, depending on the type).
Now the Heat Metal (PHB pg. 250) says;
Choose a manufactured metal object, such as a metal weapon or a suit of heavy or medium metal armour, that you can see within range. You cause the object to glow red-hot. 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. If a creature is holding or wearing the object and takes the damage from it, the creature must succeed on a Constitution saving throw or drop the object if it can.
I imagine a creature can't just drop a suit of armour it's wearing, otherwise what's the point of having the don/doff time rules, and it drops the object only if it fails the saving throw.
Even if Heat Metal only targets one piece of the armour, the obvious choice would be the shirt/breastplate if you can see it because there's other things a creature would have to take off before that.
So, is the creature trapped in their red-hot burning armour, potentially taking the extra damage for the 1 minute duration of the spell, or is there something I'm missing?
If there's strict RAW on taking armour off in less than a minute, I'll take it, but I'll happily accept answers that simply make sense provided there's an in-game time frame (1 action, 1 round, or whatever) given as well.
As for the type of armour I'm just looking at whatever's in the PHB (chainmail, half plate, full plate, breastplate, chain shirt), I don't know of any specific sub-categories or the exact size and shape.
This is of course assuming the creature tries to take of it's armour, it may not give a damn and take it like a man, but from an RP perspective I reckon it would feel like a brazen bull torture so I'm going with "they try to get out as quickly as possible".