A boiler according to the invention contains an additional air channel (9) with an inbuilt fan (10) with adjustable output. The first end (91) of the additional air channel (9) is connected with the under-stoker space (11) located outside of the wind boxes (5) of the under-stoker wind boxes system (4). The other end (9') of the additional air channel (9) is connected with either the space of the channel (6) supplying outside air to the wind boxes (5) or with the atmosphere or with the secondary air channel of the combustion chamber (2). Modernization of the existing boilers consists in installation in the described above method of an additional air channel (9) with an inbuilt fan (10). The method of elimination of uncontrolled leakages in a stoker-fired boiler consist in leading out and air, getting through air gaps, from the under-stoker space of the boiler located outside of the wind boxes (5) to the described above additional air channel (6), wherein current output of the fan (10) built into this channel is proportional to the current difference between temperature of air supplied to the wind boxes (5) and temperature of air in the additional air channel (6).