  We apply the rotation-invariant Green's function method to study the
finite-temperature properties of a $S{=}1/2$ sawtooth-chain (also called
$\Delta$-chain) antiferromagnetic Heisenberg model at the fully frustrated
point when the exchange couplings along the straight-line and zig-zag paths are
equal. We also use 13 terms of high-temperature expansion series and
interpolation methods to get thermodynamic quantities for this model. We check
the obtained predictions for observable quantities by comparison with numerics
for finite systems. Although our work refers to a one-dimensional case, the
utilized methods work in higher dimensions too and are applicable for examining
other frustrated quantum spin lattice systems at finite temperatures.
