LMC 2 has the highest X-ray surface brightness of all know supergiant shells in the Large Magellanic Cloud ( LMC ) . The X-ray emission peaks within the ionized filaments that define the shell boundary , but also extends beyond the southern border of LMC 2 as an X-ray bright spur . ROSAT HRI images reveal the X-ray emission from LMC 2 and the spur to be truly diffuse , indicating a hot plasma origin . We have obtained ROSAT PSPC and ASCA SIS spectra to study the physical conditions of the hot ( \geq 10 ^ { 6 } K ) gas interior to LMC 2 and the spur . Raymond-Smith thermal plasma model fits to the X-ray spectra , constrained by H i 21-cm emission-line measurements of the column density , show the plasma temperature of the hot gas interior of LMC 2 to be kT \sim 0.1 - 0.7 keV and of the spur to be kT \sim 0.1 - 0.5 keV . We have compared the physical conditions of the hot gas interior to LMC 2 with those of other supergiant shells , superbubbles , and supernova remnants ( SNRs ) in the LMC . We find that our derived electron densities for the hot gas inside LMC 2 is higher than the value determined for the supergiant shell LMC 4 , comparable to the value determined for the superbubble N 11 , and lower than the values determined for the superbubble N 44 and a number of SNRs .