Determining temperature inside kegerator

I kegged for the first time last Friday and I'm anxiously awaiting the results. I have an American wheat and I decided to go with the "set it and forget it" method at 12psi. My kegerator is a Sanyo 4912, which I understand is a pretty popular kegerator on this forum. I never measured my beer lines, but I'm assuming they're on the shorter side, maybe 5-6'. Hopefully I don't have to get longer lines but we'll see. From reading on this site, I've found that most people set their Sanyo fridge temp (assuming they're using the factory temp settings and not an external temp controller) on 4. I put a glass of water in overnight and went to check the temp the next day and there was a very thin layer of ice on the top. For this to happen, does that mean my kegerator temp is at or near 32 degrees? I know 32 degrees is freezing, but because only the very top layer was ice as opposed to the whole glass, do I need to turn my temp setting down? My ideal temp would be about 38-40 degrees. Thanks in advance for the help.

So I drew my first pint last night and it wasn't fully carbonated, as expected with only 6 days in the keg at 12psi. I was happy though that there was no foam! It poured perfectly so hopefully in another week it will be ready to go.