A method for repairing a high temperature composite structure fabricated from layers of composite plies. If the composite structure contains an internal high temperature core, the core is first restored by installing a core block into the damaged region, bonding the core block in place by applying high temperature material resin and uncured foam material into the region between the core block and the damaged region, and partially curing the core block. A number of repair plies, formed from pre-impregnated composite material or formed using dry cloth manually impregnated with high temperature resin are prepared. The repair plies are sized and shaped using a series of templates corresponding to the damaged region. The installed plies are cured using high temperature localized heating of the damaged region without impairing the surrounding structure.