An exhaust control system comprises a total loss determination module and a fuel control module. The total loss determination module determines a total energy loss rate of exhaust upstream of a location in an exhaust system based on a convective energy loss rate upstream of the location, a conductive energy loss rate upstream of the location, and an oxidation energy gain rate upstream of the location. The fuel control module receives a target temperature for the exhaust at the location and determines a target input energy rate based on the target temperature, a temperature of exhaust input to the exhaust system, and the total energy loss rate. The fuel control module controls a rate of fuel injection into the exhaust system upstream of an oxidation catalyst based on the target input energy rate.