  In this paper, we investigate the thermal stability and Joule-Thomson
expansion of some new qusitopological black hole solutions. We first study the
higher-dimensional static quasitopological black hole solutions in the presence
of Born-Infeld, exponential and logarithmic nonlinear electrodynamics. The
stable regions of these solutions are independent of the types of the nonlinear
electrodynamics. The solutions with the horizons relating to the positive
constant curvature, $k=+1$, have a larger region in thermal stability, if we
choose positive quasitopological coefficients, $\mu_{i}>0$. We also have a
review on the power Maxwell quasitopological black hole. Then, we obtain the
five-dimensional Yang-Mills quasitopological black hole solution and compare
with the quasitopological Maxwell solution. For large values of the electric
charge, $q$, and the Yang-Mills charge, $e$, we showed that the stable range of
the Maxwell quasitopological black hole is larger than the Yang-Mills one. This
is while thermal stability for small charges has the same behavior for these
black holes. In the following, we obtain the thermodynamic quantities for these
solutions and then study the Joule-Thomson expansion. We consider the
temperature changes in an isenthalpy process during this expansion. The
obtained results show that the inversion curves can divide the isenthalpic ones
into two parts in the inversion pressure, $P_{i}$. For $P<P_{i}$, a cooling
phenomena with positive slope happens in $T-P$ diagram, while there is a
heating process with negative slope for $P>P_{i}$. As the values of the
nonlinear parameter, $\beta$, the electric and Yang-Mills charges decrease, the
temperature goes to zero with a small slope and so the heating phenomena
happens slowly.
