Why is my TMP35 giving me weird values?
I use voltage dividers a lot and have seen this before.  

In each and every case where ALL my readings are high, yet they vary predictably (like on my solar panels - they go up during day and down at night), there has always been proven to be a very simple, single cause.

Resistance in the ground lead.  

Such as if it is plugged into a breadboard hole that is not holding it well, or if I have extended it and have connections along the way.  

So that would be the first thing I would look for.  



Having said that, if the readings are very high and do NOT vary predictably, then I would look for a disconnected ground lead.



If all the connections are good but it still misbehaves then I would swap it out with another one to make sure the part itself isn't the problem.