1. A control system for an engine of a vehicle, comprising: an adder module that determines a temperature sum based on a sum of a plurality of temperatures determined based on (i) a plurality of operating parameters of the vehicle and (ii) a plurality of predetermined values calibrated for determining an estimated temperature at a location within an exhaust system of the vehicle; a temperature difference module that determines a temperature difference based on the temperature sum and a previous value of the temperature difference; an estimating module that determines the estimated temperature at the location within the exhaust system based on the temperature difference and a reference temperature; and an actuator control module that selectively adjusts at least one engine actuator based on the estimated temperature.