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We calculate the thermal equilibrium gas temperature of high velocity clouds (HVCs) in the Galactic Halo. Our method accounts for the photoelectric heating from small grains and PAHs, and includes a detailed treatment of the ionization rates and heating due to the soft X-ray background and due to cosmic rays. Phase diagrams (thermal pressure $P$ versus gas density $n$) are presented for gas with a range of dust/gas ratios (D/G) and a range of metallicities (Z). Variations in D/G affect mainly the photoelectric heating rate, while variations in Z affect both the photoelectric heating and gas cooling. Curves are shown for D/G = 1 (local value) to D/G\al 0.005 and for Z=1 (local value) to Z$= 0.005$. We find that a two phase medium (CNM + WNM) can be in pressure equilibrium with a hot ($T\sim 1-2\times 10^{6}$ K) halo within a range of permitted pressures, $P^{\rm min}$ to $P^{\rm max}$. We take halo parameters consistent with observed properties of the soft X-ray background. In general, both $P^{\rm min}$ and $P^{\rm max}$ decrease with lower D/G due to a drop in photoelectric heating from grains, while $P^{\rm min}$ and $P^{\rm max}$ increase with lower Z due to a drop in gas coolants.
We demonstrate that successful two phase models can be constructed with pressure in the range $10^{3} \al P/k \al 10^4$ K cm$^{-3}$ consistent with the thermal pressure in the Galactic disk. In addition, using the observed relation between CNM density and distance in HVCs, ($n=75/fD_{\rm kpc}$ cm$^{-3}$; Wakker \& Schwarz 1991, AA, 250, 484) we show that our pressure curves constrain the allowed range of HVC heights to be between 0.3 - 16 kpc.
