  Using Monte Carlo methods, we compute the finite-size scaling function of the
helicity modulus $\Upsilon$ of the two-dimensional O(3) model and compare it to
the low temperature expansion prediction. From this, we estimate the range of
validity for the leading terms of the low temperature expansion of the
finite-size scaling function and for the low temperature expansion of the
correlation length. Our results strongly suggest that a Kosterlitz-Thouless
transition at a temperature $T > 0$ is extremely unlikely in this model.
