We present maps and radial profiles of the gas temperature in the nearby ga
laxy clusters A2199 and A496, which have the most accurate ASCA spectral da
ta of all hot dusters. X-ray images, temperature maps, and the presence of
moderate cooling hows indicate that these dusters are relaxed and therefore
can provide reliable X-ray mass measurements under the assumption of hydro
static equilibrium and thermal pressure support. The average cluster temper
atures corrected for the presence of cooling flows are 4.8 +/- 0.2 and 4.7
+/- 0.2 keV (90% errors), respectively, which are 10% higher than the wide-
beam single-temperature fits. Outside the central cooling-flow regions and
within r approximate to 0.7 h(-1) Mpc covered by ASCA, the radial temperatu
re profiles are similar to those of the majority of nearby relaxed dusters.
They are accurately described by polytropic models with gamma = 1.17 +/- 0
.07 for A2199 and gamma = 1.24(-0.11)(+0.88) for A496. We use these polytro
pic models to derive accurate total mass profiles. Within r = 0.5 h(-1) Mpc
, which corresponds to a radius of overdensity 1000, r(1000), for these clu
sters (estimated from our mass profiles), the total mass values are (1.45 /- 0.15) x 10(14) and (1.55 +/- 0.15) x 10(14) h(-1) M.. These values are 1
0% lower than those obtained assuming constant temperature. On the other ha
nd, the values inside a gas core radius (0.07-0.13 h(-1) Mpc) are a factor
of greater than or similar to 1.5 higher than the isothermal values. The ga
s mass fraction increases significantly with radius (by a factor of 3 betwe
en the X-ray core radius and r(1000)) and at r(1000) reaches similar values
of 0.057 +/- 0.005 and 0.056 +/- 0.006 h(-3/2) for the two clusters, respe
ctively. Our measured total mass profiles within r(1000) are remarkably wel
l approximated by the Navarro, Frenk, & White "universal" profile. Since A2
199 and A496 are typical relaxed clusters, the above findings should be rel
evant for most such systems. In particular, the observed similarity of the
temperature profiles in nearby clusters appears to reflect the underlying "
universal" dark matter profile. The upward revision of the mass values at s
mall radii for the observed temperature profile compared with those derived
assuming isothermality will resolve most of the discrepancy between the X-
ray and strong lensing mass estimates.