([@Hartman95]; [@Piran98] and references therein). These objects may be either millisecond pulsars which are arisen from accretion-induced collapse of white dwarfs in close binaries ([@Usov92]) or differentially rotating disk-like objects which are formed by the merger of a binary consisting of two neutron stars ([@Eichler89]; [@Narayan92]). Such very young fast-rotating compact objects have two possible sources of energy which may be responsible for radiation of cosmological GRBs. These are the thermal energy of the compact objects and the kinetic energy of their rotation. The thermal energy may be transformed into $\gamma$-rays by means of the following sequence of processes (for review, see [@Piran98]): (1) Emission of neutrinos and cooling of the object; (2) Absorption of neutrinos $(\nu_i +
\bar\nu_i \rightarrow e^+ + e^- )$ and formation of a fireball which mainly consists of electrons and positrons; (3) Expansion of the fireball and formation of a relativistic shell, $\Gamma_0
\gtrsim 10^2$; (4) Interaction of the shell with an external medium and acceleration of electrons to very high energies; and (5) Generation of $\gamma$-rays by high-energy electrons. The maximum thermal energy, $Q_{\rm th} ^{\rm max}$, of very young compact objects is high enough to explain the energy output of cosmological GBBs, $Q_{\rm 