A control apparatus of a compression self-ignition internal combustion engine in which fuel injected from a fuel injection valve is caused to combust by self-ignition in a combustion chamber, the control apparatus comprising: an input heat amount specification unit that, using the volume (V c (α)) of a combustion field which is a space inside the combustion chamber in which an air-fuel mixture exists and being combusted, the temperature (Th α) before the start of combustion in the combustion field, a combustion field target temperature (T N) for limiting the amount of NOx produced during combustion in the combustion field to a predetermined target NOx production amount, the density of gas (p) existing in the combustion field, and the specific heat (σ) of gas existing in the combustion field as parameters, specifies an amount of heat input to the combustion chamber according to which the flame temperature during combustion in the combustion field becomes the combustion field target temperature (T N); and an input heat amount adjustment unit that adjusts an amount of heat (Q(α)) input to the combustion chamber using the input heat amount specified by the input heat amount specification unit as a maximum value of the input heat amount, wherein the input heat amount specification unit is configured so as to partition a period of combustion in the combustion chamber into a plurality of micro-periods, and specify the amount of heat input to the combustion chamber according to which the flame temperature of the combustion field becomes the combustion field target temperature (T N) in each of the micro-periods, wherein the amount of heat Q(α) input to the combustion chamber is set so as to be less than or equal to the maximum value of the input heat amount according to the inequality: Q α ≤ ρ α σ α V C α T N − Th α where α is a representative value of a crank angle in a micro-period, V c (α) is the volume of the combustion field being a space occupied by a spray of fuel injected in the micro-period, Th α is the temperature of the air-fuel mixture existing in the combustion field at the time when fuel injection was performed in the micro-period, ρ(α) is the density of the gas in the combustion field in the micro-period, σ(α) is the specific heat of the gas in the combustion field in the micro-period, T N is a target combustion temperature in the combustion field in the micro-period, and Q(α) is the input heat amount to the combustion chamber in the micro-period. an input heat amount specification unit that, using the volume (V c (α)) of a combustion field which is a space inside the combustion chamber in which an air-fuel mixture exists and being combusted, the temperature (Th α) before the start of combustion in the combustion field, a combustion field target temperature (T N) for limiting the amount of NOx produced during combustion in the combustion field to a predetermined target NOx production amount, the density of gas (p) existing in the combustion field, and the specific heat (σ) of gas existing in the combustion field as parameters, specifies an amount of heat input to the combustion chamber according to which the flame temperature during combustion in the combustion field becomes the combustion field target temperature (T N); and an input heat amount adjustment unit that adjusts an amount of heat (Q(α)) input to the combustion chamber using the input heat amount specified by the input heat amount specification unit as a maximum value of the input heat amount, wherein the input heat amount specification unit is configured so as to partition a period of combustion in the combustion chamber into a plurality of micro-periods, and specify the amount of heat input to the combustion chamber according to which the flame temperature of the combustion field becomes the combustion field target temperature (T N) in each of the micro-periods, wherein the amount of heat Q(α) input to the combustion chamber is set so as to be less than or equal to the maximum value of the input heat amount according to the inequality: Q α ≤ ρ α σ α V C α T N − Th α where α is a representative value of a crank angle in a micro-period, V c (α) is the volume of the combustion field being a space occupied by a spray of fuel injected in the micro-period, Th α is the temperature of the air-fuel mixture existing in the combustion field at the time when fuel injection was performed in the micro-period, ρ(α) is the density of the gas in the combustion field in the micro-period, σ(α) is the specific heat of the gas in the combustion field in the micro-period, T N is a target combustion temperature in the combustion field in the micro-period, and Q(α) is the input heat amount to the combustion chamber in the micro-period.