  The matrix element of the electromagnetic current between pion states is
calculated in quenched lattice QCD at a temperature of $T = 0.93 T_c$. The
nonperturbatively improved Sheikholeslami-Wohlert action is used together with
the corresponding ${\cal O}(a)$ improved vector current. The electromagnetic
vertex function is extracted for pion masses down to $360 {\rm MeV}$ and
momentum transfers $Q^2 \le 2.7 {\rm GeV}^2$.
