Abstract: One of these distilling apparatus (10) comprises two columns, an evaporation column (14) and a condensation column (16), separated by a partition (18) equipped with rows of slits dividing them into 4 distillation stages. The evaporation column (14) comprises plates with hydrophilic or wettable faces, and the condensation column comprises rectangular hollow-plate (21) heat exchangers (221-6). Cold water ascends in these exchangers and saturated humid hot air descends in the condensation column (16). A perforated sheet (251-4) increases the uniformity of the partial airflows descending between the plates. The water is heated in a boiler (34); the hot water is scattered at the top of the evaporation column and the air cooled in the condensation column is sucked downwards by a fan (34). The air flows in a closed circuit. Performance is maximised, after the top temperature TE2 (45 to 90° C.