  When two identical fermions exchange their positions, their wave function
gains phase factor $-1$. We show that this distance-independent effect can
induce nonlocal entanglement in one-dimensional (1D) electron systems having
Majorana fermions at the ends. It occurs in the system bulk and has nontrivial
temperature dependence. In a system having a single Majorana at each end, the
nonlocal entanglement has a Bell-state form at zero temperature and decays as
temperature increases, vanishing suddenly at certain finite temperature. In a
system having two Majoranas at each end, it is in a cluster-state form and its
nonlocality is more noticeable at finite temperature. By contrast, thermal
states of corresponding 1D spins do not have nonlocal entanglement.
