You are clearly not talking about MySQL. CREATE TEMPORARY TABLE simply creates a physical table on disk that is destroyed at the end of the session, which can be created with any storage engine. Explicit temporary tables are handled just like "regular" tables and is dependent upon the storage engine (w/ MyISAM, indexes are stored in the key buffer, InnoDB keeps both recently accessed data and indexes in the InnoDB buffer pool).
KEY and INDEX are literally the exact same thing and are just there to support different syntaxes: http://dev.mysql.com/doc/refman/5.1/en/alter-table.html
Perhaps you are referring to primary keys vs secondary indexes, for which there is a difference in how they are physically stored on disk and in memory, particularly with InnoDB. There is a substantial performance gain to be had by having a relevant primary key that is referenced in the where clause as the data is stored in the same page as the primary key, both on disk and in the buffer pool. Secondary indexes reference the primary key, thus require two lookups.