Great question. Depending on which brand of thermal cooker you have. For example, whether it’s a Saratoga Jacks brand or the Thermos brand will make a bit of a difference. Because the Saratoga Jacks brand lid does twist closed a bit. Not super securely, but a bit. The Thermos brand lid is held shut by the handle being closed in a certain position. But if it tipped over, it could open. One thing to note is the description of thermal cookers being vacuum sealed is not in regards to the lid being secure for transit. The vacuum seal is regarding the way the outer pot has been made to help retain temperature. So, with any thermal cooker, you will want to secure it to remain upright so as to not tip over in a car ride.

Great question. I am not aware of any thermal cooker having a thermometer with it. For my personal use, I have just bought a quality thermometer from some place such as Harbor Freight and it has worked fine.