Just a straight hookup is all you need. The washers shouldn't affect the performance of the thermometer, but they are not needed. The thermometer gets its reading from the tip or maybe last 1/4" of the thermometer probe. If nothing else, a washer on the front, between the dial and lid will just make it stick out and look odd.
Just drill the correct hole/holes if not already there and install it with the thermometer and wing nut.