H_3_^+^ is a ubiquitous and important astronomical species whose spectrum has been observed in the interstellar medium, planets and tentatively in the remnants of supernova SN1897a. Its role as a cooler is important for gas giant planets and exoplanets, and possibly the early Universe. All this makes the spectral properties, cooling function and partition function of H_3_^+^ key parameters for astronomical models and analysis. A new high-accuracy, very extensive line list for H_3_^+^ called MiZATeP was computed as part of the ExoMol project alongside a temperature-dependent cooling function and partition function as well as lifetimes for excited states. These data are made available in electronic form as supplementary data to this article and at www.exomol.com.