when using a temp gun you need to hold it a bit farther away from the spot you're measuring (5-7" i think? it said something like that with the directions) and hold the trigger down for a few seconds. i'm not sure about what brand of temp gun you're using, but with my equipment i'd trust the temp gun over my AcuRite.
i can almost guarantee that climbing the probe won't be an issue.
for the water resistance: IMO i wouldn't worry about it. they may not be water proof, but unless they're literally submerged in urine for a lengthy period of time i wouldn't worry about it.