There are conditions for carrying hair curlers and curling irons on board as well as checking them in as checked baggage.
You can carry these on board or check them in.
Those that are filled with hydrocarbon gas and have a safety cover firmly attached to the heat source can be carried on board or checked in.

* Up to 1 per person
* Refillable gas cartridges cannot be carried on board or checked in.

Those for which the battery or batteries can be removed from the main unit can be carried on board or checked in.
Measures must be taken to ensure removed batteries and spare batteries do not short circuit.
Wired hair curlers and curling irons for which the battery or batteries cannot be removed from the main unit cannot be carried on board or checked in.

* In the case of lithium batteries, only removed batteries can be carried on board.