Looks like it will work, start it up and see how it functions . See if the temperature is constant and there should be a drop in temp when there's a drop in room temp. Give it a good test before adding eggs.
Check to see if your thermometer is alcohol or mercury. If its silver ( mercury ), you need to be EXREMEMLY careful not to break it . All of the microbiology labs that I work in , now , have removed all the old mercury thermometers due to the potential contamination issue.
You could simply choose to replace it with a digital thermometer.
one time i found a pile of old thermostats, i'm guessing they took it out cuz the mercury, so i broke them all open and put all the mercury on the road
and then it came together and formed one huge ball it was the sickest thing i've ever seen