And..........how do you know the mercury thermometer is actually accurate?
Unless you have access to a calibrated thermometer traceable to a national standard, your best option would be to:
-ice/water bath to set 0C
-slowly boiling water to set 100C.
On the last measurement, you would have to adjust the temperature for the height above sea level from where you live. The higher elevation, the lower the temperature water will boil.
https://www.engineeringtoolbox.com/boiling-points-water-altitude-d_1344.html
Also, make sure the water is as free as possible of dissolved salts. Purchase some distilled water to perform your experiments.