  We develop an optimized perturbation theory for the Ginzburg - Landau
description of thermal fluctuations effects in the vortex liquids. Unlike the
high temperature expansion which is asymptotic, the optimized expansion is
convergent. Radius of convergence on the lowest Landau level is $a_{T}=-3$ in
2D and $a_{T}=-5$ in 3D. It allows a systematic calculation of magnetization
and specific heat contributions due to thermal fluctuations of vortices in
strongly type II superconductors to a very high precision. The results are in
good agreement with existing Monte Carlo simulations and experiments.
Limitations of various nonperturbative and phenomenological approaches are
noted. In particular we show that there is no exact intersection point of the
magnetization curves both in 2D and 3D.
