We explore the effectiveness of the Brink-Axel hypothesis for the computation of stellar electron capture and $\beta$-decay rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow-Teller (GT) strength distributions for a selection of $sd$--shell nuclides, using two different microscopic models, namely the proton-neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into %We later performed the calculation of weak-interaction mediated rates in stellar matter, specifically electron capture and $\beta$-decay rates, for a range of densities $10 \, \mathrm{g/cm^3} \leq\rho \leq10^{11} \, \mathrm{g/cm^3} $ and range of temperatures $1 \, \mathrm{GK} \leq T \leq 30 \, \mathrm{GK}$. When transitions from excited states were approximated using the Brink-Axel hypothesis, augmented by so-called `back-resonance' transitions, the rates were affected by up to 3 orders of magnitude or more at high temperatures and densities. Thus the Brink-Axel hypothesis is not a reliable approximation for the calculation of stellar rates, especially in high temperature--density environments.
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