Is the Soviet spacecraft Luna 16 still working and transmitting temperature & radiation levels? Attempts to Google the results of Luna 16 have failed, possibly because the results are in Russian.
No. The Luna 16 descent stage used batteries and transmitted until the batteries ran out .
Twenty-six hours after landing, explosive bolts were fired above the Luna 16 descent stage. On a jet of flame, the upper stage shot off€ and headed towards the white and blue Earth hanging in the distance. It headed straight up, motor still purring, building up to lunar escape velocity, its radio pouring out details from the four aerials poking out the side. The Sea of Fertility returned to the quiet it had known for eons. The descent stage was the only forlorn reminder of the brief visit. The lower stage on the moon continued to transmit signals for a couple of days until the battery ran out. Only two instruments seem to have been carried: a thermometer and radiation counter.
 Soviet and Russian Lunar Exploration - Brian Harvey, page 243