We develop a theory of the conductance of a quantum dot connected to t
wo leads by single-mode quantum point contacts. If the contacts are in
the regime of perfect transmission, the conductance shows no Coulomb
blockade oscillations as a function of the gate voltage. In the presen
ce of small reflection in both contacts, the conductance develops smal
l Coulomb blockade oscillations. As the temperature of the system is l
owered, the amplitude of the oscillations grows, and eventually sharp
periodic peaks in conductance are formed. Away from the centers of the
peaks the conductance vanishes at low temperatures as T-2, in agreeme
nt with the theory of inelastic cotunneling developed for the weak-tun
neling case. Conductance near the center of a peak can be studied usin
g an analogy with the multichannel Kondo problem. In the case of symme
tric barriers, the peak conductance at T --> 0 is of the order of <e(2
)/(h)over bar>. In the asymmetric case, the peak conductance vanishes
linearly in temperature.