  In [5], the notion of polynomial cocycles is used to give an expression for
the second cohomology of T-groups with coefficients in a torsion-free nilpotent
module. We make this expression concrete in the case of a T-group G of
nilpotency class <=2 and coefficients in a trivial G-module, using a Lie
algebra associated to the group. This approach allows us to construct explicit
cocycles representing the elements of the second cohomology group.
