We study the temperature structure of the rich cluster of galaxies Abe
ll 1367 using two independent methods of correcting for the ASCA point
-spread function. The results of the two methods are in excellent agre
ement and give solid evidence of a strong and localized shock in the i
ntracluster medium. Our analysis suggests that we are observing the me
rger of two subclusters. We find that the lower luminosity subcluster,
located to the northwest, has a higher temperature of 4.2 +/- 0.3 keV
, compared to the more luminous southeast subcluster, whose temperatur
e is 3.2 +/- 0.1 keV. An analysis of the ROSAT surface brightness prof
iles of both subclusters is also presented. The data agree well with p
redictions from numerical simulations of mergers between subcluster-si
zed masses, in particular with early stages of the merger prior to the
first core passage.