The temporary tables prefixed with a single # are scoped within a single database connection.  Thus if you have 10 hits on your website then you might have 10 concurrent database connections (being simple here - no pooling or other voodoo ).  Each connection can have its own temp table.  Thus the use of temp tables within the stored proc should not cause any problem.

A global temporary table (prefix ##) IS shared - much like a standard fixed table in the database.