  The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most
challenging problems in the field of highly frustrated quantum magnetism.
Stimulated by the seminal paper of M.~Planck [M.~Planck, Verhandl. Dtsch. phys.
Ges. {\bf 2}, 202-204 (1900)] we calculate thermodynamic properties of this
model by interpolating between the low- and high-temperature behavior. For that
we follow ideas developed in detail by B.~Bernu and G.~Misguich and use for the
interpolation the entropy exploiting sum rules [the ``entropy method'' (EM)].
We complement the EM results for the specific heat, the entropy, and the
susceptibility by corresponding results obtained by the finite-temperature
Lanczos method (FTLM) for a finite lattice of $N=32$ sites as well as by the
high-temperature expansion (HTE) data. We find that due to pronounced
finite-size effects the FTLM data for $N=32$ are not representative for the
infinite system below $T \approx 0.7$. A similar restriction to $T \gtrsim 0.7$
holds for the HTE designed for the infinite PHAF. By contrast, the EM provides
reliable data for the whole temperature region for the infinite PHAF. We find
evidence for a gapless spectrum leading to a power-law behavior of the specific
heat at low $T$ and for a single maximum in $c(T)$ at $T\approx 0.25$. For the
susceptibility $\chi(T)$ we find indications of a monotonous increase of $\chi$
upon decreasing of $T$ reaching $\chi_0 \approx 0.1$ at $T=0$. Moreover, the EM
allows to estimate the ground-state energy to $e_0\approx -0.52$.
