  We present a study of heat and charge transport in
Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$ focused on the size of the low-temperature
linear term of the thermal conductivity at optimal doping level. In the
superconducting state, the magnitude of this term implies a d-wave gap with an
amplitude close to what has been reported. In the normal state, recovered by
the application of a magnetic field, measurement of this term and residual
resistivity yields a Lorenz number $L = \kappa_{N}\rho_{0}/T = 1.3 \pm 0.2
L_{0}$. The departure from the value expected by the Wiedemann-Franz law is
thus slightly larger than our estimated experimental resolution.
