Neutron-induced reactions on unstable isotopes play a key role in the nucleosynthesis $i$--, $r$--, $p$--, $rp$-- and $\nu p$--processes occurring in astrophysical scenarios. While direct cross section measurements are possible for long-living unstable isotopes using the neutron Time-of-Flight method, the currently available neutron intensities ($\approx10^{6}$ n/s) require large samples which are not feasible for shorter lifetime isotopes... For the last four decades, the $^{7}$Li$(p,n)$ reaction has been used to provide a neutron field at a stellar temperature of $\approx$ 0.3 GK with significantly higher intensity, allowing the successful measurement of many cross sections along the $s$-process path. In this paper we describe a novel method to use this reaction to produce neutron fields at temperatures of $\approx$ 1.5-3.5 GK, relevant to scenarios such as convective shell C/Ne burning, explosive Ne/C burning, and core-collapse supernovae. This method will allow direct cross section measurements of many important reactions at explosive temperatures, such as $^{26}$Al$(n,p)$, $^{75}$Se$(n,p)$ and $^{56}$Ni$(n,p)$. (read more)