A climate control apparatus for a cleanroom livestock building includes a supply air unit, comprising a supply air conveyor device, an exhaust air unit comprising an exhaust air conveyor device, a temperature sensor, an air pressure sensor, and a climate control unit. The climate control apparatus is adapted to reduce the volume of air conveyed by the exhaust air unit whenever the air pressure detected by the air pressure sensor falls below a predetermined lower air pressure limit value, increase the volume of air conveyed by the exhaust air unit whenever the air pressure detected by the air pressure sensor exceeds a predetermined upper air pressure limit value, and increase the volume of air conveyed with the supply air unit when the temperature detected by the temperature sensor exceeds a predetermined first upper temperature limit value.