  We analyze the finite-temperature effects on the phase diagram describing the
insulating properties of interacting 1D bosons in a quasi-periodic lattice. We
examine thermal effects by comparing experimental results to exact
diagonalization for small-sized systems and to density-matrix renormalization
group (DMRG) computations. At weak interactions, we find short thermal
correlation lengths, indicating a substantial impact of temperature on the
system coherence. Conversely, at strong interactions, the obtained thermal
correlation lengths are significantly larger than the localization length, and
the quantum nature of the T=0 Bose glass phase is preserved up to a crossover
temperature that depends on the disorder strength. Furthermore, in the absence
of disorder, we show how quasi-exact finite-T DMRG computations, compared to
experimental results, can be employed to estimate the temperature, which is not
directly accessible in the experiment.
