We examine the impact of gas pressure on the transverse coherence of high-redshift ( 2 \leq z \leq 4 ) Lyman- \alpha forest absorption along neighboring lines of sight that probe the gas Jeans scale ( projected separation \Delta r _ { p } \leq 500 h ^ { -1 } kpc comoving ; angular separation \Delta \theta \lesssim 30 \arcsec ) . We compare predictions from two smoothed particle hydrodynamics ( SPH ) simulations that have different photoionization heating rates and thus different temperature-density relations in the intergalactic medium ( IGM ) . We also compare spectra computed from the gas distributions to those computed from the pressureless dark matter . The coherence along neighboring sightlines is markedly higher for the hotter , higher pressure simulation , and lower for the dark matter spectra . We quantify this coherence using the flux cross-correlation function and the conditional distribution of flux decrements as a function of transverse and line-of-sight ( velocity ) separation . Sightlines separated by \Delta \theta \lesssim 15 \arcsec are ideal for probing this transverse coherence . Higher pressure decreases the redshift-space anisotropy of the flux correlation function , while higher thermal broadening increases the anisotropy . In contrast to the longitudinal ( line-of-sight ) structure of the Ly \alpha forest , the transverse structure on these scales is dominated by pressure effects rather than thermal broadening . With the rapid recent growth in the number of known close quasar pairs , paired line-of-sight observations offer a promising new route to probe the IGM temperature-density relation and test the unexpectedly high temperatures that have been inferred from single sightline analyses .