It's not so impossible, except for making holes and installing thermocouples, but you can get even closer like this - turn it on to the maximum, wait until it heats up, turn it off immediately and direct it through the glass to the diode and the board around the pyrometer. So we will see the temperature of the crystal itself and the board around it. Turning off the flashlight is necessary only in order not to mislead the pyrometer. Reflector and glass can be removed for greater accuracy. A high-quality pyrometer Testo / Fluke costs about $ 40-100, which is not a problem these days.
Can also take a pyrometer from the nearest hospital for one evening or measure the temperature of the lantern right in their yard so that they don't think that we want to steal it.