  We study the magnetocaloric effect for the integrable antiferromagnetic
Heisenberg spin chain with competing interactions. We computed the Gr\"uneisen
parameter, which is closely related to the magnetocaloric effect, for the
quantum spin chain in the thermodynamical limit. This is obtained by means of
the solution of a set of non-linear integral equations, which describes the
thermodynamics of the model. We also provide results for the entropy $S$ and
the isentropes in the $(H,T)$ plane.
