  An analysis of efficiency and its bounds at maximum work output for
Carnot-like heat engines is conducted. The heat transfer processes are
described by the linear law with time-dependent heat conductance. The upper
bound of efficiency is found to be the CA efficiency,and is independent of the
time duration completing each process and the time-dependent conductance. We
prove that even the working medium exchanges heat sufficiently with the heat
reservoirs, the work which could be extracted is finite and limited. The
optimal temperature profiles in the heat exchanging processes are also
analyzed. When the dimensionless contact times satisfy certain relations,the
endoreversible model is recovered.
