Motivated by the spin-triplet superconductor Sr2RuO4, the thermal Hall conductivity is investigated for several pairing symmetries with broken time-reversal symmetry. In the chiral p-wave phase with a fully opened quasiparticle excitation gap, the temperature dependence of the thermal Hall conductivity has a temperature linear term associated with the topological property directly, and an exponential term, which shows a drastic change around the Lifshitz transition. Examining f-wave states as alternative candidates with $bm d=Delta_0hat{z}(k_x^2-k_y^2)(k_xpm ik_y)$ and $bm d=Delta_0hat{z}k_xk_y(k_xpm ik_y)$ with gapless quasiparticle excitations, we study the temperature dependence of the thermal Hall conductivity, where for the former state the thermal Hall conductivity has a quadratic dependence on temperature, originating from the linear dispersions, in addition to linear and exponential behavior. The obtained result may enable us to distinguish between the chiral p-wave and f-wave states in Sr2RuO4.
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