  We analyze the temperature evolution of the anomalous magnetic spectrum of
the spin-1/2 triangular quantum Heisenberg antiferromagnet, which is proximate
to a quantum critical point. Recently, its low energy excitations have been
identified with two-spinon bound states, well defined in an ample region of the
Brillouin zone. In this work, we compute the thermal magnetic spectrum within a
Schwinger boson approach, incorporating Gaussian fluctuations around the
saddle-point approximation. In order to account for a finite N\'eel temperature
$T_N$, we incorporate an exchange interaction between triangular layers. As
temperature rises, the dispersion relation of the two-spinon bound states,
representing single-magnon excitations, remains unchanged but becomes mixed
with the thermally activated spinon continuum. Consequently, a crossover occurs
at a temperature $T^* \simeq 0.75 T_N$, defining a "terminated Goldstone
regime" between $T^*$ and $T_N$, where only the Goldstone modes survives as
well-defined magnon excitations, up to the N\'eel temperature. Our results
support the idea that the fractionalization of magnons near a quantum critical
point can be extended to more realistic quasi-2D frustrated antiferromagnets.
