  Quantum thermodynamics is a promising route to unambiguous detections of
Majorana bound states. Being fundamentally different from quantum transport,
this approach reveals unique Majorana thermodynamic behavior and deepens our
insight into Majorana quantum transport itself. Here we demonstrate that a
nanoscopic system with topological superconductors produces a remarkable
accumulation of Majorana thermodynamic states in wide ranges of Majorana
tunneling phases by means of increasing its temperature $T$. Revealing this
physical behavior is twofold beneficial. First, it significantly reduces the
dependence of the entropy on the tunneling phases which become almost
irrelevant in experiments. Second, the fractional Majorana entropy
$S_M^{(2)}=k_B\ln(2^\frac{3}{2})$ may be observed at high temperatures
substantially facilitating experiments. Analyzing quantum transport, we predict
that when the temperature increases, the above thermodynamic behavior will
induce an anomalous increase of the linear conductance from vanishing values up
to the unitary fractional Majorana plateau $G_M=e^2/2h$ extending to high
temperatures.
