After a long development break, we managed to put more time into the project and solved (or at least seems we did) the issue with the Peltier element not behaving as expected. Turns out we were too shy with our power supply and the element needed more juice to run properly.

Using a 10V 2A power supply together with a 38X38X20mm heat dissipater and a 40X40X10mm 12V fan we were able to make it maintain 15°C on the top surface for 10 minutes (and still very stable) in a room at 28°C. The same configuration allows us to heat up the same surface to 35°C. Both temperatures (15 and 35°C) are the extreme values used for the experiments we want to conduct with this device.