  In a recent paper [M. Huber {\it et al}, Phys. Rev. Lett. {\bf 104}, 210501
(2010)] new criteria to find out the presence of multipartite entanglement have
been given. We exploit these tools in order to study thermal entanglement in a
spin-star network made of three peripheral spins interacting with a central
one. Genuine tripartite entanglement is found in a wide range of the relevant
parameters. A comparison between predictions based on the new criteria and on
the tripartite negativity is also given.
