  We present an overview of the recently suggested cosmological model driven by
conformal field theory (CFT) with the initial conditions in the form of the
microcanonical density matrix. In particular, we discuss the origin of
inflationary stage in this model and a novel feature -- the thermal nature of
the primordial power spectrum of the CMB anisotropy. The relevant effect of
"temperature of the relic temperature anisotropy" can be responsible for a
thermal contribution to the red tilt of this spectrum, additional to its
conventional vacuum component. The amplification of this effect due to recently
established $a$-theorem in CFT is briefly discussed.
