It is shown that the temperature \(\theta\) (x,t) of a slab \(0\leq x\leq L\) of unit thickness, defined in a half-strip \(S(t_ 0)=[0,1]\times [t_ 0,\infty]\) of a x,t-plane, has the maximum property if there is a net flow of heat out of the slab at each instant, and that \(\theta\) has the minimum property if there is a net flow into the slab at each moment, so long as we concentrate on a half-strip \(S(t_ 0)\), where \(t_ 0\geq 0\) is some finite number chosen appropriately.