Here is a IR picture of the full moon taken a while back with a Fluke TiR.
If I remember correctly, there are ca 9 pixels covering the lunar disk, and that should theoretically be enough to get a somewhat accurate reading, disregarding the influence of the atmosphere of earth and of course the reflected temperature of the sun on the moon.
According to my TIR, the temperature is ca 55 ' Celcius.
If the modded E4 has the double FOV (45') and the double resolution, the results should possibly be similar using the E4 with similar IFOV.
Imaging Performance Fluke TiR:
Field of View ....................................................... 23 ° x 17 °
Spatial Resolution (IFOV)................................... 2.5 mRad
Minimum Focus Distance
Thermal Lens.................................................. 15 cm (approx. 6 in)
Visible (Visual) Light Lens .............................. 46 cm (approx. 18 in)
Focus.................................................................. Manual
Image Frequency................................................ 9 Hz refresh rate
Detector Type ..................................................... 160 X 120 Focal Plane Array,
uncooled microbolometer
Infrared Lens Type.............................................. 20 mm EFL, F/0.8 lens