  We study the probabilistic (conditional) teleportation protocol when the
entanglement needed to its implementation is given by thermal entanglement,
i.e., when the entangled resource connecting Alice and Bob is an entangled
mixed state described by the canonical ensemble density matrix. Specifically,
the entangled resource we employ here is given by two interacting spin-1/2
systems (two qubits) in equilibrium with a thermal reservoir at temperature T.
The interaction between the qubits is described by a Heisenberg-like
Hamiltonian, encompassing the Ising, the XX, the XY, the XXX, and XXZ models,
with or without external fields. For all those models we show analytically that
the probabilistic protocol is exactly equal to the deterministic one whenever
we have no external field. However, when we turn on the field the probabilistic
protocol outperforms the deterministic one in several interesting ways. Under
certain scenarios, for example, the efficiency (average fidelity) of the
probabilistic protocol is greater than the deterministic one and increases with
increasing temperature, a counterintuitive behavior. We also show regimes in
which the probabilistic protocol operates with relatively high success rates
and, at the same time, with efficiency greater than the classical limit 2/3, a
threshold that cannot be surpassed by any protocol using only classical
resources (no entanglement shared between Alice and Bob). The deterministic
protocol's efficiency under the same conditions is below 2/3, highlighting that
the probabilistic protocol is the only one yielding a genuine quantum
teleportation. We also show that near the quantum critical points for almost
all those models the qualitative and quantitative behaviors of the efficiency
change considerably, even at finite T.
