Exhaust purifying apparatus and method for purifying exhaust

An exhaust purifying apparatus (11) includes regeneration control means. The control means regenerates a catalyst (32,33) by combusting and removing particulate matter deposited on the catalyst (32,33) when catalyst regeneration requirements are all satisfied. The requirements include at least a requirement related to a temperature of the catalyst (32,33) and a requirement related to an amount of heat removed by air that passes through the catalyst (32,33). Therefore, the apparatus (11) reliably prevents the exhaust gas purification function of the catalyst (32,33) from being spoiled by the excessive temperature rising caused by the removal of the particulate matter from the catalyst (32,33).