In this work we study the warm equation of state of asymmetric nuclear matter in the quark-meson coupling model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar, vector, and isovector mesons. Mechanical and chemical instabilities are discussed as a function of density and isospin asymmetry. The binodal section, essential in the study of the liquid-gas phase transition is also constructed and discussed. The main results for the equation of state are compared with two common parametrizations used in the nonlinear Walecka model and the differences are outlined.