An intake air heating system for a vehicle , the system comprising: an electrical switching device configured to selectively connect a battery of the vehicle to a resistor of an air heater in contact with intake air of the vehicle ; and a control circuit configured to in response to an enable signal from an engine controller , drive the electrical switching device to connect the battery to the resistor of the air heater at full current; measure a resistance of the resistor of the air heater indicative of an initial temperature of the resistor ; and estimate a temperature increase by: repeatedly measuring a present value of current through the electrical switching device or repeatedly computing an average of current measured over a period of time; accumulating a current squared value of the measured current values or the averages; estimating the temperature increase based on the accumulated current squared value; estimate a temperature of the resistor of the air heater based on a sum of the initial temperature of the resistor and the temperature increase; and in response to the estimated temperature of the resistor of the air heater exceeding a desired temperature value, modulate the electrical switching device to reduce current from the battery of the vehicle to the resistor . an electrical switching device configured to selectively connect a battery of the vehicle to a resistor of an air heater in contact with intake air of the vehicle ; and a control circuit configured to in response to an enable signal from an engine controller , drive the electrical switching device to connect the battery to the resistor of the air heater at full current; measure a resistance of the resistor of the air heater indicative of an initial temperature of the resistor ; and estimate a temperature increase by: repeatedly measuring a present value of current through the electrical switching device or repeatedly computing an average of current measured over a period of time; accumulating a current squared value of the measured current values or the averages; estimating the temperature increase based on the accumulated current squared value; estimate a temperature of the resistor of the air heater based on a sum of the initial temperature of the resistor and the temperature increase; and in response to the estimated temperature of the resistor of the air heater exceeding a desired temperature value, modulate the electrical switching device to reduce current from the battery of the vehicle to the resistor . in response to an enable signal from an engine controller , drive the electrical switching device to connect the battery to the resistor of the air heater at full current; measure a resistance of the resistor of the air heater indicative of an initial temperature of the resistor ; and estimate a temperature increase by: repeatedly measuring a present value of current through the electrical switching device or repeatedly computing an average of current measured over a period of time; accumulating a current squared value of the measured current values or the averages; estimating the temperature increase based on the accumulated current squared value; repeatedly measuring a present value of current through the electrical switching device or repeatedly computing an average of current measured over a period of time; accumulating a current squared value of the measured current values or the averages; estimating the temperature increase based on the accumulated current squared value; estimate a temperature of the resistor of the air heater based on a sum of the initial temperature of the resistor and the temperature increase; and in response to the estimated temperature of the resistor of the air heater exceeding a desired temperature value, modulate the electrical switching device to reduce current from the battery of the vehicle to the resistor . <EOS>