  In this paper, we consider the monodromy and, in particularly, the
isomonodromy sets of accessory parameters for the Heun class equations. We show
that the Heun class equations can be obtained as limits of the linear systems
associated with the Painlev\'{e} equations when the Painlev\'e transcendents go
to one of the actual singular points of the linear systems. While the
isomonodromy sets of accessory parameters for the Heun class equations are
described by the Taylor or Laurent coefficients of the corresponding
Painlev\'{e} functions, or the associated tau functions, at the positions of
the critical values. As an application of these results, we derive some
asymptotic approximations for the isomonodromy sets of accessory parameters in
the Heun class equations, including the confluent Heun equation, the
doubly-confluent Heun equation and the reduced biconfluent Heun equation.
