The internal temperature is what you want and, since there is a built-in sensor on the chip, why not use it. The sensor is typically a forward biased silicon diode which has a fairly repeatable voltage to temperature value when biased with a small constant current. If you use the Shockley ideal diode voltage equation versus current and temperature, you should be close enough to the actual temperature for engineering purposes. If you measure the diode forward voltage at room temperature at the desired diode current as a calibration point, then you can use the diode equation to determine the temperature from the forward voltage at other temperatures.