  Using analytic methods and $1$-D two-fluid simulations, we study the effect
of cosmic rays (CRs) on the dynamics of interstellar superbubbles (ISBs) driven
by multiple supernovae (SNe)/stellar winds in OB associations. In addition to
CR advection and diffusion, our models include thermal conduction and radiative
cooling. We find that CR injection at the reverse shock or within a central
wind-driving region can affect the thermal profiles of ISBs and hence their
X-ray properties. Even if a small fraction ($10-20\%$) of the total mechanical
power is injected into CRs, a significant fraction of the ram pressure at the
reverse shock can be transferred to CRs. The energy transfer becomes efficient
if (1) the reverse shock gas Mach number exceeds a critical value ($M_{\rm
th}\gtrsim 12$) and (2) the CR acceleration time scale $\tau_{\rm acc}\sim
\kappa_{\rm cr}/v^2$ is shorter than the dynamical time, where $\kappa_{\rm
cr}$ is CR diffusion constant and $v$ is the upstream velocity. We show that CR
affected bubbles can exhibit a volume averaged hot gas temperature
$1-5\times10^{6}$ K, lower by a factor of $2-10$ than without CRs. Thus CRs can
potentially solve the long-standing problem of the observed low ISB
temperatures.
