DS18B20 - Thermometer and Sensor discrepancy (varying)
Can you buy a few more from other (more reliable) sellers ? Perhaps it is damaged. Did you accidently connect it wrong and it got very hot ?

There has been counterfeit DS18B20 sensors, but they were transistors that were re-labeled as DS18B20. Those didn't work at all.

You have not convinced me that you are only measuring the air temperature. Maybe there is still something nearby that causes it to get warmer. The 3 degrees difference is a lot. There must be a good reason for that, or else the DS18B20 is broken. How accurate is that mercury thermometer ? 

I wrote before: "To be sure you can put it in distilled water at sea level at 0°C (water and ice cubes) and 100°C (boiling water)". That is what I did, out of curiosity. It turned out to be accurate.