Heat conduction in silicon nanowires that exhibit a diameter constriction are studied from a Monte Carlo technique used to solve the phonon Boltzmann transport equation. Through the tailoring of the constriction shape, it is shown that thermal conductivity of the nanostructures can be lowered and adjusted. The phonon mean free path related to boundary scattering then becomes a key parameter. The calculation of the thermal conductance through the constriction is also performed and in the case of ''steep'' constriction , the ballistic and diffusive transport regimes through an aperture are recovered depending on the size of the constriction. Temperature dependence of the thermal conductivity in such constricted structures is addressed and dominant scattering processes are evaluated. Eventually, the case of a ''long con-striction'' is simulated and a lowering of thermal conductivity, as compared to simple nanowires, is observed and discussed.