  Jupiter's enhancement in nitrogen relative to hydrogen when compared to the
Sun has been interpreted as evidence that its early formation occurred beyond
the N$_{2}$ snowline ($\sim$ 20-40 AU). However, the rapid growth necessary to
form Jupiter before the dissipation of the solar nebula would lead to the
forming planet's core reaching very high temperatures ($>$1000 K), which would
lead to it warming its surroundings. Here, we explore the effects of a luminous
planetary core on the solids that it ultimately accretes. We find that a
critical transition occurs where very hot (rapidly accreting) cores drive off
volatiles prior to accretion, while cool cores (slowly accreting) are able to
inherit volatile rich solids. Given Jupiter's nitrogen enrichment, if it formed
beyond the N$_{2}$ snowline, its core could not have accreted solids at a rate
above 10$^{-10}$ M$_{\odot}$ yr$^{-1}$. Our results suggest that either Jupiter
formed in more distal regions of the solar nebula, or nitrogen loss was
suppressed, either by its incorporation in more refractory carriers or because
it was trapped within ices which devolatilized at higher temperatures.
