An oven thermometer sits on the cooking grates or "oven" grate. It does not go into the meat. You can't see it while the lid is on which is it's only downfall, but it cost just a couple bucks and can be picked up probably at your grocery store. Everyone should have a couple.
If you're looking for monitoring the cooking temp. as well the meat temps, then you should look into the Maverick lineups. They are more costly, and range anywhere from $20 to $100 USD.
The lid thermometers lie to you, mostly. Heat rises so the readings can be very different from cooking grate temps, which is the important one.
Take a look at the Mavericks and see if that's a route you are interested in. Otherwise the oven thermos and quite frankly, your hand can be one of the best judgements of temp.
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