An exhaust control system comprises a nominal specific heat module, a correction module, a specific heat determination module, and a convective loss estimation module. The nominal specific heat module determines a nominal specific heat of exhaust input to a component of an exhaust system based on a temperature of the exhaust input to the component and based on a predetermined oxygen content. The correction module determines a specific heat correction based on an oxygen content measured by a sensor. The specific heat determination module determines a specific heat of the exhaust based on the nominal specific heat and the specific heat correction. The convection loss estimation module estimates a convective energy loss rate associated with the component based on the specific heat.