The question of the multiplicity of steady states in a non-isothermal CSTR in which an infinite number of Arrhenius first-order continuous reactions is taking place is addressed here. It is shown that only for some degenerate cases does an infinite number of steady states exist, whereas, in general, the behaviour of the system is similar to the discrete case. Two particular feed concentration distributions have been considered, namely a Gamma-distribution for the energies of activation and a Gamma-distribution for the preexponential factor : for these situations, the discrete counterpart turns out to be the single-component case, since either one or three steady states exist. Finally, multiplicity regions have been compared for different values of the distribution parameter and of the average Damkohler number.