Interstellar molecules preferentially reside in denser, cooler, optically shielded portions of the interstellar medium, but a weak residue of H2 will form via purely gas-phase processes involving H(-) even in rather bare atomic gas, the so-called warm interstellar medium where the temperature (>1000 K) and electron fraction (0.01 to 0.1) are relatively high. Along with H2, a few trace molecules will also form in this gas, partially because strongly endothermic reactions such as C(+) + H2 → CH(+) + H are energetically allowed. The observed abundance patterns of SH(+), CH(+) and OH(+) are reproduced by the warm gas chemistry, but not their overall abundances with respect to hydrogen. Even the very smallest molecular hydrogen fractions observed in the Milky Way along sightlines of low mean density are well above those that can readily be produced in the warm interstellar medium by gas-phase or grain-surface H2 formation processes. This suggests that density inhomogeneities may obscure the molecular contribution of warmer gas.