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In this paper in terms of the replica method we consider the high temperaturelimit of (2+1) directed polymers in a random potential and propose an approachwhich allows to compute the scaling exponent $\theta$ of the free energyfluctuations as well as the left tail of its probability distribution function.It is argued that $\theta = 1/2$ which is different from the zero-temperaturenumerical 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 isnon-universal being temperature dependent.

On the scaling properties of (2+1) directed polymers in the high temperature limit