In the standard inflationary paradigm, the seeds for cosmic structures are assumed to be of quantum origin. During inflation, the quantum fluctuations of the fields are stretched by the cosmic expansion to macroscopic sizes and become classical, then growing through gravitational collapse to eventually form the structures we observe today. Thermal fluctuations introduce another possible origin for small inhomogeneities. In the early universe the temperatures could be very high, and there are several important cosmological models where thermal fluctuations could be the main ingredient responsible for seeding the inhomogeneities. In this work it is suggested a general phenomenological parametrization for a class of early universe models described by an effective equation of state which is a function of the Hubble parameter. In such models, the main seeds of cosmological fluctuation are thermal fluctuations that can appear even at classical level. The proposed effective equation of state leads to a description of the universe which have the advantage of avoiding the initial singularity problem and also the problems associated with reheating, providing a smooth transition from an era with w e f f∼− 1 to an era with w= 1/3. Motivated by the formalism previously developed in the literature to compute the spectrum from thermal fluctuations [1], we compute for this class of models, the power spectrum of scalar and tensor perturbations, in addition to non-gaussianity parameters, which allows us to constraint the free parameters of this class of models with the observational results.