Suppose that I want to measure the temperature of an object, such as a pot of hot water. When I stick the thermometer into the pot, I know that the temperature measured by the thermometer is its own temperature when it reaches thermal equilibrium, which, according to the Zeroth Law of Thermodynamics, is equal to the temperature of the object (the pot of hot water) at thermal equilibrium. Does this imply that the temperature of the object that I am now measuring is different than the initial temperature, and if so, is the change significant? Also, can I somehow use the information of the system at thermal equilibrium to find the initial temperature of the object?
Yes. The amount differs by the method used, as well as the dominant heat transfer mechanism (conduction, convection or radiation).
Therfore even a thermal imaging camera draws/emits heat from/towards the object.
If you use a temperature measuring device that has mass, the answer is "yes", you slightly changed the temperature of the pot of water. If you use a temperature measuring device that doesn't have mass, such as an infra-red thermometer, the answer would be "no", since you didn't contact the water with anything that has any thermal inertia. Regarding how much the temperature changed in the first case, you have to use calorimetry to solve for the final temperature. Examples of calorimetry can be found at
Yes the thermometer affects the temperature of the body that you are measuring. The change in temperature can be found doing some simple calorimetry (so you have to know the temperature, mass, and specific heat of the thermometer before you use it). And the change in temperature might be significant (but typically isn't at all), it just depends. Suppose you are measuring the temperature of a very small amount of a low specific heat substance and your thermometer is particularly cold (or hot, relative to the material of interest); here the change in temperature might be significant. Again, understanding how much the temperature will change just boils down to calorimetry.
Short answer is "yes" but in general is insignificant.