  We study Coulomb blockade oscillations of thermoelectric coefficients of a
single electron transistor based on a quantum dot strongly coupled to one of
the leads by a quantum point contact. At temperatures below the charging energy
E_C the transport of electrons is dominated by strong inelastic cotunneling. In
this regime we find analytic expressions for the thermopower as a function of
temperature T and the reflection amplitude $r$ in the contact. In the case when
the electron spins are polarized by a strong external magnetic field, the
thermopower shows sinusoidal oscillations as a function of the gate voltage
with the amplitude of the order of $e^{-1}|r|\frac{T}{E_C}$. We obtain
qualitatively different results in the absence of the magnetic field. At
temperatures between $E_C$ and $E_C|r|^2$ the thermopower oscillations are
sinusoidal with the amplitude of order $e^{-1}|r|^2 \ln \frac{E_C}{T}$. On the
other hand, at $T\ll E_C|r|^2$ we find non-sinusoidal oscillations of the
thermopower with the amplitude $\sim e^{-1} |r| \sqrt{T/E_C} \ln(E_C/T)$.
