It is from a nautical term. Keel is part of a ship. If a ship is level and evenly balanced in the water then it is even-keeled. If a person is even-keeled, then they are of a calm temperament.

From a thesaurus: .....calm, composed, even-tempered, imperturbable, peaceful, placid, serene, stable, steady, unexcitable, well-balanced.... The image is one of a boat which stays steady on the water.