  The anomalous thermodynamic properties of the paradigmatic frustrated
spin-1/2 triangular lattice Heisenberg antiferromagnet (TLH) has remained an
open topic of research over decades, both experimentally and theoretically.
Here we further the theoretical understanding based on the recently developed,
powerful exponential tensor renormalization group (XTRG) method on cylinders
and stripes in a quasi one-dimensional (1D) setup, as well as a tensor product
operator approach directly in 2D. The observed thermal properties of the TLH
are in excellent agreement with two recent experimental measurements on the
virtually ideal TLH material Ba$_8$CoNb$_6$O$_{24}$. Remarkably, our numerical
simulations reveal two crossover temperature scales, at $T_l/J \sim 0.20$ and
$T_h/J\sim 0.55$, with $J$ the Heisenberg exchange coupling, which are also
confirmed by a more careful inspection of the experimental data. We propose
that in the intermediate regime between the low-temperature scale $T_l$ and the
higher one $T_h$, the gapped "roton-like" excitations are activated with a
strong chiral component and a large contribution to thermal entropies, which
suppress the incipient 120$^\circ$ order that emerges for temperatures below
$T_l$.
