We study the transport properties of quantum dots and quantum point contacts in the Coulomb blockade regime and in the limit where the quantum point contact has nearly fully transmitting channels. Using a transformation to a multichannel Tomonaga-Luttinger-type model, we find the scaling behavior of the junction close to pinchoff. It is shown that the junction scales to an insulating junction. We find a crossover between a low-temperature regime with Coulomb blockade to a high-temperature regime where the quantum charge fluctuations are dominant. The crossover temperature between these regimes is given by Tc∼U[1-G0/NGH]N/2, where U are the bare charging energy, G0 is the nominal conductance, N is the number of channels, and GH=e2/h.