As a promising platform for unconventional superconductivity, Josephson junctions (JJs) of tetradymite topological insulators (TIs) and s-wave superconductors have been investigated in recent years. This family of TI materials, however, often suffers from spurious bulk transport, which hampers the observation of the exotic physics of their topological surface states. Thus, disentangling the transport mechanism of bulk and surface contributions in TI JJs is of high importance when investigating proximity induced superconductivity in those crystals. In this work, we add to the insights regarding these contributions by studying the temperature-dependent behaviour of a Bi2Te3-based JJ with transparent interfaces. In electrical transport measurements, we investigate differential conductance spectra of multiple Andreev reflections (MARs) and find a qualitative temperature-dependent change from peak features at low temperatures to dip features at higher ones. The observation of both kind of MAR patterns in a single JJ suggests contributions of diffusive bulk and ballistic surface states and links to a similar finding in the temperature dependence of the critical current. Our work advances the research of induced superconductivity in TIs and offers new avenues to study the induced superconductivity in the topological surface states of these materials.