  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$(n,p)$.
