  We investigate thermal entanglement between two non-nearest-neighbor sites in
ferromagnetic Heisenberg chain and on fractal lattices by means of the
decimation renormalization-group (RG) method. It is found that the entanglement
decreases with increasing temperature and it disappears beyond a critical value
T_{c}. Thermal entanglement at a certain temperature first increases with the
increase of the anisotropy parameter {\Delta} and then decreases sharply to
zero when {\Delta} is close to the isotropic point. We also show how the
entanglement evolves as the size of the system L becomes large via the RG
method. As L increases, for the spin chain and Koch curve the entanglement
between two terminal spins is fragile and vanishes when L\geq17, but for two
kinds of diamond-type hierarchical (DH) lattices the entanglement is rather
robust and can exist even when L becomes very large. Our result indicates that
the special fractal structure can affect the change of entanglement with system
size.
