  Recently, we have investigated the dynamics of the universe in tachyon
cosmology with non-minimal coupling to matter \cite{faraj}-\cite{faraj3}. In
particular, for the interacting holographic dark energy (IHDE), the model is
studied in \cite{Ravanpak}. In the current work, a significant observational
program has been conducted to unveil the model's thermodynamic properties. Our
result shows that the IHDE version of our model better fits the observational
data than $\Lambda$CDM model. The first and generalized second thermodynamics
laws for the universe enveloped by cosmological apparent and event horizon are
revisited. From the results, both first and generalized second laws,
constrained by the observational data, are satisfied on cosmological apparent
horizon.In addition, the total entropy is verified with the observation only if
the horizon of the universe is taken as apparent horizon. Then, due to validity
of generalized second law, the current cosmic acceleration is also predicted.
