  We study a thermal engine model for which Newton's cooling law is obeyed
during heat transfer processes. The thermal efficiency and its bounds at
maximum output power are derived and discussed. This model, though quite
simple, can be applied not only to Carnot engines but also to four other types
of engines. For the long thermal contact time limit, new bounds, tighter than
what were known before, are obtained. In this case,this model can simulate
Otto, Joule Brayton, Diesel, and Atkinson engines. While in the short contact
time limit, which corresponds to the Carnot cycle, the same efficiency bounds
as Esposito et al's are derived. In both cases, the thermal efficiency
decreases as the ratio between the heat capacities of the working medium during
heating and cooling stages increases. This might provide instructions for
designing real engines.
