Systems and methods for estimating a temperature calibration are described. One embodiment of a method includes determining, by a computing device, a current speed of the vehicle and determining a dynamic smoothing number, the dynamic smoothing number being dependent on the current speed, the dynamic smoothing number being utilized to determine an estimated temperature of an air injection system. Some embodiments include calculating the estimated temperature of the air injection system from the dynamic smoothing number, determining whether the estimated temperature is greater than a predetermined temperature of the air injection system, and in response to determining that the estimated temperature is greater than the predetermined temperature of the air injection system, sending a signal for on-board diagnostics to resume at a next start.