A general frame work is devised to obtain the specific heat of nonequilibrium systems described by the energy-landscape picture, where a representative point in the phase space is assumed to obey a stochastic motion which is governed by a master equation. The specific heat depends on the observation time and becomes quenched one for short observation time and annealed one for long observation time. In order to test its validity, the frame work is applied to a two-level system where the state goes back and forth between two levels stochastically. The specific heat is shown to increase from zero to the Schottky form as the observation time is increased from zero to infinity. The anomaly of specific heat at the glass transition is reproduced by a system with a model energy-landscape, where basins of the landscape form a one-dimensional array and jump rate between adjacent basins obeys a power-law distribution. It is shown that the glass transition can be understood as a transition from an annealed to a quenched system and that the glass transition temperature becomes lower when the observation time is increased.