A diesel engine exhaust gas after-treatment device comprising a first temperature sensor that detects the temperature either upstream or downstream from a filter as a first temperature and detects the filter's other temperature as a second temperature, and a microcomputer. The microcomputer calculates the filter's hypothetical bed temperature from the temperature of either of the first and second temperatures; calculates the heat radiation coefficient from the filter to the external atmosphere according to the exhaust gas flow rat; and calculates the second temperature's estimated temperature based on the heat radiation coefficient and the above-described one first temperature. The filter's estimated bed temperature is found based on the above-described hypothetical bed temperature and the above-described detected second temperature and the above-described second temperature's estimated temperature. The microcomputer regenerates the filter based on the estimated bed temperature.