Abstract: The linear analytic theory of small scale -size thermal blooming instabilities for a high energy laser propagating through a homogeneous medium is derived in paraxial scalar wave approximation and isobaric supposition. When we perform Fourier transforms in transversal coordinates and Laplace transforms in time and longitudinal coordinate, the fluctuations can be obtained in analytic form. In the real world the Fourier components of the fluctuations are written with the propagation kernal (or Green function) K_k (z,t), after the inverting Laplace transforms are performed.