We consider the pairing of massless Dirac electrons and holes located on opposite surfaces of thin films of "strong" three-dimensional topological insulators. Such pairing is predicted to give rise to a topological exciton condensate with unusual properties. We estimate the quantitatively achievable critical temperature of the pairing while taking into account the self-consistent screening of the Coulomb interaction, disorder, and hybridization of electron and hole states caused by tunneling through the film. The increase of the gap above the hybridization value when the temperature is lowered can be an observable signature of the pairing. System parameters required to observe the electron-hole pairing are discussed.