If there was a blacksmith wearing a great kilt, and there were probably a few that did, I could see him taking it off if he were worried about it catching sparks. Traditionally, a long tailed shirt was worn under it and that would be enough to preserve modesty. The leather apron would have been worn over that. Since he's working at the forge, I doubt if he would be too concerned about being cold. When he was ready to leave the forge, he could put the great kilt back on.

After the era of the great kilt, the blacksmith probably wore trousers.