Interest in the superconducting proximity effect has been reinvigorated recently by novel optoelectronic applications as well as by the possible emergence of the elusive Majorana fermion at the interface between topological insulators and superconductors. Here we produce high-temperature superconductivity in Bi(2)Se(3) and Bi(2)Te(3) via proximity to Bi(2)Sr(2)CaCu(2)O(8+δ), to access higher temperature and energy scales for this phenomenon. This was achieved by a new mechanical bonding technique that we developed, enabling the fabrication of high-quality junctions between materials, unobtainable by conventional approaches. We observe proximity-induced superconductivity in Bi(2)Se(3) and Bi(2)Te(3) persisting up to at least 80 K-a temperature an order of magnitude higher than any previous observations. Moreover, the induced superconducting gap in our devices reaches values of 10 mV, significantly enhancing the relevant energy scales. Our results open new directions for fundamental studies in condensed matter physics and enable a wide range of applications in spintronics and quantum computing.