Molten carbonate electrolyzers (MCECs) represent an innovative method for the conversion of electrical energy into chemical energy, coupling the advantages of both low- and high-temperature electrolysis processes. In the present work, a planar MCEC was experimentally tested under different temperature, gas flow rate and composition conditions. A 2D model was developed for the first time and validated against experimental data. The model was found to accurately describe the behavior of the cell, both in terms of the relationship between applied voltage and flowing current and of product gas composition. The model was then used to predict thermal effects in case of adiabatic operation of the cell, showing that, in the absence of temperature control, the cell temperature could increase significantly and that the presence of thermochemical reactions alongside the electrochemical processes could significantly affect the behavior of the cell.