  We show that the compact self avoiding walk configurations, kinetically
generated by the recently introduced Interacting Growth Walk (IGW) model, can
be considered as members of a canonical ensemble if they are assigned random
values of energy. Such a mapping is necessary for studying the thermodynamic
behaviour of this system. We have presented the specific heat data for the IGW,
obtained from extensive simulations on a square lattice; we observe a broad
hump in the specific heat above the $\theta$-point, contrary to expectation.
