  It is commonly believed that the significant energy saving advantages are
belonged to the logic circuits which operate at low temperature as less enegy
is needed for cooling them to the treshold temperature after operation. Also,
nanoscale thermal management, efficient energy usage in nanoscale and
especially thermal optimization are the most challenging issues, while dealing
with the new generation of transistors as the miniaturizing unlimitedly the
silicon channels of the transistors has resulted in an increase in the energy
consumption of computers and the leakage currents. In this paper, the
non-Fourier thermal attitudes of well-known two-dimensional crystalline
materials of graphene, blue phosphorene, germanene, silicene and MoS$_2$ as the
silicon channels replacements are studied by using the phonon Monte-Carlo
method. We show that graphene and blue phosphorene have the least maximum
temperature, representer of the reliability of the transistors, among the all
five investigated nano-channels during the Monte-Cralo simulation. The
established hotspots of these two materials are always cooler, not reaching the
temperature threshold level, and they lose the heat much faster as the heat
generation zone is switched off. The obtained results considered along with the
electrical disadvantages of the graphene layer, suggests the blue phosphorene
as the more thermally appropriate and optimal choice for the silicon channel
replacement in new designed field effect transistors. That is to say that the
limit of the energy and economic cost of the producing the advanced blue
phosphorene chips meets the value of the product for the computing enterprise.
