  In this paper in terms of the replica method we consider the high temperature
limit of (2+1) directed polymers in a random potential and propose an approach
which allows to compute the scaling exponent $\theta$ of the free energy
fluctuations as well as the left tail of its probability distribution function.
It is argued that $\theta = 1/2$ which is different from the zero-temperature
numerical value which is close to 0.241. This result implies that unlike the
$(1+1)$ system in the two-dimensional case the free energy scaling exponent is
non-universal being temperature dependent.
