  In this article we derive a priori error estimates for the $hp$-version of
the mortar finite element method for parabolic initial-boundary value problems.
Both semidiscrete and fully discrete methods are analysed in $L^2$- and
$H^1$-norms. The superconvergence results for the solution of the semidiscrete
problem are studied in an eqivalent negative norm, with an extra regularity
assumption. Numerical experiments are conducted to validate the theoretical
findings.
