We study the high-temperature behavior of an intermediate-statistics fermionic gas model whose quantum statistical properties enable us to effectively deduce the details about both the interaction among deformed (quasi) particles and their anyonic behavior. Starting with a deformed fermionic grand partition function, we calculate, in the thermodynamical limit, several thermostatistical functions of the model such as the internal energy and the entropy by means of a formalism of the fermionic q calculus. For high temperatures, a virial expansion of the equation of state for the system is obtained in two and three dimensions and the first five virial coefficients are derived in terms of the model deformation parameter q. From the results obtained by the effect of fermionic deformation, it is found that the model parameter q interpolates completely between bosonlike and fermionic systems via the behaviors of the third and fifth virial coefficients in both two and three spatial dimensions and in addition it characterizes effectively the interaction among quasifermions. Our results reveal that the present deformed (quasi) fermion model could be very efficient and effective in accounting for the nonlinear behaviors in interacting composite particle systems.