An exhaust purification system comprising: a fuel injection amount acquisition unit, configured to acquire a fuel injection amount of a vehicle; a temperature acquisition unit, configured to acquire a temperature of a catalyst for reducing and purifying nitrogen compounds in an exhaust; a temperature control unit, configured to control the temperature of the catalyst by controlling an intake amount or an exhaust amount passing through the catalyst, or by increasing an after injection amount; and an execution control unit configured to receive the acquired fuel injection amount from the fuel injection amount acquisition unit, and to receive the acquired temperature of the catalyst from the temperature acquisition unit; wherein, the execution control unit is further configured to determine if the acquired temperature of the catalyst is lower than a predetermined temperature threshold; and when the execution control unit determines that the temperature of the catalyst is lower than the predetermined temperature threshold, the execution control unit is configured to transit the temperature control unit to a temperature rise mode, on condition of at least one of: (i) the fuel injection amount is determined to be equal to or greater than a first threshold determined based on the load that is applied to the engine; (ii) a change amount of the fuel injection amount within a predetermined time is equal to or greater than a second threshold by which it is determined that a shift is executed by the vehicle; or (iii) the fuel injection amount is less than a third threshold determined based on a load applied to the vehicle; wherein the execution control determines each of the first, second, and third thresholds based on a rotational speed of an engine; and wherein, upon transition to the temperature rise mode, the temperature control unit increases the exhaust temperature by controlling an intake amount or an exhaust amount by using an intra-exhaust pipe injection, a post injection, or an intake throttle using an intake throttle, to increase the temperature of the catalyst. a fuel injection amount acquisition unit, configured to acquire a fuel injection amount of a vehicle; a temperature acquisition unit, configured to acquire a temperature of a catalyst for reducing and purifying nitrogen compounds in an exhaust; a temperature control unit, configured to control the temperature of the catalyst by controlling an intake amount or an exhaust amount passing through the catalyst, or by increasing an after injection amount; and an execution control unit configured to receive the acquired fuel injection amount from the fuel injection amount acquisition unit, and to receive the acquired temperature of the catalyst from the temperature acquisition unit; wherein, the execution control unit is further configured to determine if the acquired temperature of the catalyst is lower than a predetermined temperature threshold; and when the execution control unit determines that the temperature of the catalyst is lower than the predetermined temperature threshold, the execution control unit is configured to transit the temperature control unit to a temperature rise mode, on condition of at least one of: (i) the fuel injection amount is determined to be equal to or greater than a first threshold determined based on the load that is applied to the engine; (ii) a change amount of the fuel injection amount within a predetermined time is equal to or greater than a second threshold by which it is determined that a shift is executed by the vehicle; or (iii) the fuel injection amount is less than a third threshold determined based on a load applied to the vehicle; (i) the fuel injection amount is determined to be equal to or greater than a first threshold determined based on the load that is applied to the engine; (ii) a change amount of the fuel injection amount within a predetermined time is equal to or greater than a second threshold by which it is determined that a shift is executed by the vehicle; or (iii) the fuel injection amount is less than a third threshold determined based on a load applied to the vehicle; wherein the execution control determines each of the first, second, and third thresholds based on a rotational speed of an engine; and wherein, upon transition to the temperature rise mode, the temperature control unit increases the exhaust temperature by controlling an intake amount or an exhaust amount by using an intra-exhaust pipe injection, a post injection, or an intake throttle using an intake throttle, to increase the temperature of the catalyst.