Despite its name, high-temperature superconductivity still occurs at cryogenic temperatures. The main difference from low-temperature superconductivity is usually that 'high-Tc' superconductors can use liquid nitrogen (at 77K) as a coolant while low-temperature superconductors always need liquid helium (4.2K) temperatures and below.
Most prominent materials in the high-Tc range are the so-called cuprates, i.e. YBCO (Yttrium-Barium-Copper-Oxide) and related substances.