NO no no no NO... The type of thermometer in the pic is an instant read type. They are not designed to be left in the oven, smoker etc. There are others designed to do just that, but that ain't one of them.
That type of probe is used for getting a quick temp. its not designed to be put in an oven and left for a long period. it's a calibratedable thermometer as well and i would not trust it holding temp in that kind of situation.