A home laundry drier (1) having a revolving drum (5) for housing the laundry to be dried, a hot-air generator (7) for circulating a stream of hot air inside the drum (5), and a steam generator (17) for feeding steam into the drum (5); the steam generator (17) having an electric boiler (18) designed to receive a given quantity of water and immediately convert it into a stream of low-pressure steam to be fed into the drum (5), a demineralized-water reservoir (20) located over and communicating with the electric boiler (18), and a lint filter (23) located upstream from the water reservoir (20); the water reservoir (20) receiving distilled water from the water canister (12) of the heat exchanger (10) of the hot-air generator (7) via a water drain circuit (13); and the laundry drier (1) also having a liquid level sensor (26) for determining when the water in the water reservoir (20) is below a given minimum level, and a central control unit (24) for determining whether the water reservoir (20) is in a given low-water-level condition at both the start and end of a user-selected drying cycle not including activation of the steam generator (17).