Magnetic tunnel junctions ͑MTJs͒ with crystalline MgO barriers are currently being used in a variety of applications, namely forefront magnetic sensors and memories. In this work we probed the temperature ͑T͒ dependence of the transport and magnetic properties of MgO-based MTJs with different CoFeB free layer thicknesses ͑t fl = 1.55, 1.65, 1.95, and 3.0 nm͒. All samples have the same insulating MgO barrier with a nominal thickness of 1.35 nm. Our results show that the tunnel magnetoresistance ͑TMR͒ temperature behavior is mainly due to a strong variation of the conductance ͑G͒ of the antiparallel state. Also, we provide evidence that direct elastic tunneling is the dominant mechanism determining the temperature dependence of the tunneling conductance and TMR in the studied MgO MTJs. Intrinsic to this mechanism is the thermal smearing of the electron energies near the Fermi level which then plays a key role in G͑T͒, especially in the parallel state where the overall change in G is very small. Furthermore, we show a clear change in the MTJ properties as the free layer thickness is reduced. Besides the typical decrease of TMR related with the loss of spin polarization, we were able to probe the thickness dependence of the spin wave ␣ parameter. MTJ with the thinner free layer show both absence of hysteresis in the room temperature TMR cycles and interesting freezing effects in the zero and field cool magnetization curves at low temperatures, revealing the discontinuous nature of thin free layers.