Why do you think that's important, or even relevant?1
You have already been told (by someone who has already run the experiment) that the effect you say you wish to understand will become clear within an hour of starting the experiment.2
That convection will be negligible if you place your insulated thermometers within a vacuum. You would want to suspend them within the vacuum using thin supports of a good thermal insulator.3If I may step back from such details for a moment: You appear determined to obstruct your learning process by pursuing call-to-perfection fallacies.4If you were thinking like a scientist, you'd want to find out. To find out, you'd conduct an experiment.5
1. A sphere in orbit will experience a heat gain/loss cycle related to the period of rotation and revolution (no cycle at all of the rotation period equals the revolution period). Whatever the cycle, the center will be at a constant temperature if the body is spherical and uniform and the orbit is (nearly) circular. A thermometer on the surface of an airless body will experience the same cycle.
2. Then on Earth you will have witnessed only 1/24 th of the relevant data.
3. What moves the mercury? Radiative heat from the wall of the vacuum chamber. What warms the wall? Ambient air temperature and solar radiation.
4. I'd say "clean experiments".