No! This thermometer should not be left in food which is cooking, either in the oven, on the grill or on the stove top. It is an instant read thermometer, so you can take a reading very quickly, and then remove it.
You can insert the thermometer for long enough to take a good reading – which is about 5 seconds. You can even leave it in the meat for 10, 15 or 20 seconds if you are unsure of the reading; but that really is not necessary. It will give an accurate reading in about 5 seconds. Then press the ‘HOLD’ button and remove the thermometer and it will still show the temperature reading.