We have derived expressions for the thermally induced meandering of domain walls in two-dimensional lattices with a square or triangular symmetry and isotropic nearest neighbour interactions. The derived expressions for the thermally induced meandering are universal, i.e. they only depend on the reduced temperature, T/TC, where TC is the phase transition temperature. The universal expressions for the domain wall meandering can easily be compared with experimental microscopic data and allow the exact determination of the phase transition temperature at temperatures well below the actual phase transition temperature. We anticipate that our approach can be generalized to more complex lattices having interactions that go beyond nearest neighbours.