Give a ``constructive solution'' of Example 2 of Section 4.1. Your solution may be based on the following procedure for achieving maximum temperature of the hot body. A thermodynamic engine is operated between the two cooler bodies, extracting work until the two cooler bodies reach a common temperature. This work is then used as the input to a heat pump, extracting heat from the cooler pair and heating the hot body. Show that this procedure leads to the same result as was obtained in the example.