  We use spherically symmetric hydrodynamic simulations to study the dynamical
evolution and internal structure of superbubbles (SBs) driven by clustered
supernovae (SNe), focusing on the effects of thermal conduction and cooling in
the interface between the hot bubble interior and cooled shell. Our simulations
employ an effective diffusivity to account for turbulent mixing from nonlinear
instabilities that are not captured in 1D. The conductive heat flux into the
shell is balanced by a combination of cooling in the interface and evaporation
of shell gas into the bubble interior. This evaporation increases the density,
and decreases the temperature, of the SB interior by more than an order of
magnitude relative to simulations without conduction. However, most of the
energy conducted into the interface is immediately lost to cooling, reducing
the evaporative mass flux required to balance conduction. As a result, the
evaporation rate is typically a factor of $\sim$3-30 lower than predicted by
the classical similarity solution of Weaver et al. (1977), which neglects
cooling. Blast waves from the first $\sim$30 SNe remain supersonic in the SB
interior because reduced evaporation from the interface lowers the mass they
sweep up in the hot interior. Updating the Weaver solution to include cooling,
we construct a new analytic model to predict the cooling rate, evaporation
rate, and temporal evolution of SBs. The cooling rate, and hence the hot gas
mass, momentum, and energy delivered by SBs, is set by the ambient ISM density
and the efficiency of nonlinear mixing at the bubble/shell interface.
