Once a spell is cast, its effects aren't limited by its range, unless
the spell's description says otherwise. (PHB p. 203)
You have to be within 60' to heat the metal. After that, the onus is on the target to either break your concentration, or get out of the armor/drop the metal object. Concentration is the limiting factor on this spell. You have one minute (10 turns of combat) maximum to do as much damage as you can with this spell ... and anything that breaks your concentration ends it.
The Sage Advice clears this up, per Jeremy Crawford.
You don’t need to be within line of sight or within range to maintain
concentration on a spell, unless a spell’s description or other game
feature says otherwise.
If, as a DM, you think this is too powerful of an effect, you could houserule this to where the bonus action to keep the damage going requires you to be within 60' of range, but as written, the spell does not require that in the spell description on page 250 of the PHB. IMO, the concentration requirement is sufficient to keep it within the box. At lower levels, it might seem overpowered for single creature targets: against a mob, the number of times you might get hit and need to make a concentration check acts as a counter. At higher levels the damage is less telling on the target and the concentration requirement (consider all of those other spells you may want to be using) begins to factor in to a greater amount.