Depending on the temperature range the thermometer is meant to measure, Richard you might be able to reattach it by using the freezer comparment, most domestic freezers go down to about -15C so if the lower mark on your thermometer is -5C it may be reachable, the object is to contract the mercury into the little expansion chamber at the top of the reservoir, If you use the Heating up method BE VERY CARFUL it is real easy to blow the end off the thermometer also Remember if the thermometer reads up to ,say 105C then boiling water wlill not reach it!!! you may need to use cooking oil with the associated hazards!11 The common "mistakes" made when carrying out these steps are
1 Hot glass looks EXACTLY the same as cold glass
2 Glass that has been in the freezer at -15C degrees for several hours will BURN as effectively as a flame
3 when heating anyting point it AWAY from people,self and any valuable paintings, crockery etc.