How should a thermometer be sterilized?

Digital thermometers should have a plastic sleeve, but even with that, you should use an alcohol swab to thoroughly wet, rub it and allow it to air dry after each use. Some of the digitals will have battery and "mother board" problems if you wash them in soapy water. The old-timey Mercury thermometers and modern non-digital thermometers can be soaked in alcohol over night or washed with warm soapy water and then swabbed with alcohol, allowed to dry and returned to their cases.

Since you can get digital thermometers for less than 10.00, it is a good idea to have a thermometer for each person in your family....and if you are really germ-phobic you can replace them after every illness...but that is overkill, IMO.