We present GHRS intermediate and high-resolution (FWHM approximate to 11-20 and approximate to 3.5 km s(-1)) absorption line observations of atoms in the interstellar gas toward the Galactic halo stars HD 18100 (l = 217.degrees 9, b = -62.degrees 7, d approximate to 3.1 kpc) and HD 100340 (l = 258.degrees 8, b = +61.degrees 2, d approximate to 5.3 kpc). The neutral gas absorption toward HD 18100 occurs in 10 components spanning velocities from approximate to-70 to +30 km s(-1). Two components near V-LSR = -7 and -3 km s(-1) contain much of the neutral gas and have T approximate to 3000-4000 K. The average gas-phase abundances for the sight line are close to solar for some elements (S, P, and Zn) and substantially less than solar for others (Mg, Si, Mn, Cr, Fe, and Ni). The observed abundance pattern resembles that found for paths through the warm neutral medium of the Galactic disk and halo. An inferred abundance ratio of (Mg + Fe)/Si approximate to 3.1 for the dust grains in the clouds implies that the grain cores probably consist of silicates plus various oxides and/or pure Fe. The absorption toward HD 100340 spans the velocity range from -75 to + 80 km s(-1); the S, Mg, Mn, and Ni abundances in the principal components near -30, -18, and -2 km s(-1) are similar to those toward HD 18100. Using measures of absorption out of the collisionally excited C II P-2(3/2) level, we estimate C II cooling rates for the HD 18100 and HD 100340 directions that agree with results from UV observations of two other high-latitude sight lines and IR measures of 157 mu m line emission at high latitudes. The average C II cooling rate of 2.2 x 10(-26) ergs s(-1) H-atom(-1) along halo sight lines is several times smaller than for the typical disk sight line and is consistent with a mixture of gas types in a Galactic halo with P/k = 2000 K cm(-3), assuming photoelectric heating from small grains and PAHs is the dominant heating mechanism. The value of [n(e)] approximate to 0.071 cm(-3) estimated from C II* absorption toward HD 18100 is similar to values found toward HD 93521 and 3C 273. The warm neutral medium along these halo sight lines is probably associated with higher ionization gas at similar velocities. Possible sites for the high-ionization gas include warm-hot gas interfaces and turbulent mixing layers. Toward HD 100340, we find low column density, partially ionized components near +31, +59, and +78 km s(-1). The source of ionization in these components is probably O and B star radiation similar to that believed to be producing the extended H alpha emitting layer in the Galaxy.