Based on the generalized uncertainty principle (GUP) with the modication of the phase space, the partition function has recently been modied . In the present work, we analyze the self-consistency of the axiomatic thermodynamic derived from the modied partition function. This work studies the self-consistency for the thermodynamic quantities pressure, energy density, entropy, number density and some correlated quantities. The thermal parameters at the moment of freeze-out are extracted, as well as the occupation number of the fermionic states. We found that, the deformed phase space distribution does not obey the thermodynamic consistency conditions. On the other hand, the thermodynamic quantities and freeze-out parameters are well reproduced.