무더위, mudeowi, is not simply bad heat. It is 물, water, fastened to 더위, heat: heat with the wet in it.
Korean keeps the two apart. 불볕더위 is fire-glare heat, the sort that stings the skin under a hard sun and lets go the moment you get into shade. Mudeowi is the other kind. It wraps round you and does not let go after dark.
The words for it are damp themselves. 무덥다. 후텁지근하다. 푹푹 찐다. Your back starts going sticky just saying them.
People got through this without air conditioning for a very long time, and what they had was the vocabulary.