We investigate transport and shot noise in lateral N-TI-S contacts, where N is a normal metal, TI is a Bi-based three dimensional topological insulator (3D TI), and S is an s-type superconductor. In normal state, the devices are in the elastic diffusive transport regime, as demonstrated by a nearly universal value of the shot noise Fano factor $F_{rm N}approx1/3$ in magnetic field and in reference normal contact. In the absence of magnetic field, we identify the Andreev reflection (AR) regime, which gives rise to the effective charge doubling in shot noise measurements. Surprisingly, the Fano factor $F_{rm AR}approx0.22pm0.02$ is considerably reduced in the AR regime compared to $F_{rm N}$, in contrast to previous AR experiments in normal metals and semiconductors. We suggest that this effect is related to a finite thermal conduction of the proximized, superconducting TI owing to a residual density of states at low energies.
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