The thermometer should be sanitized and dry. Thermometers are not usually disposable. This means that they can be reused. It does not mean that you are not going to properly sanitize it whenever you use it.
A thermometer will hold residue from the past user whether it is dead skin, hair, and so much more. It may affect the temperature reading and it will not be sanitary to leave that behind. To properly sanitize, the thermometer should be washed thoroughly, soaped, rinsed and dried completely before use. Simply using an alcohol to clean the thermometer will not work.
When working with a penetrating thermeter. Residue exists on the thermometer. Sanitizing does not clean a thermometer; therefore the residue must be removed by washing. After washing, rinse soap off of the device, sanitize and air dry.