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.