A DFT computational mechanistic study of the [2+2+2] cyclotrimerization of a diyne with benzonitrile, catalyzed by a cobalt complex, has been carried out. Three alternative catalytic cycles have been examined together with the precatalytic step (responsible for the induction period). The favored mechanism takes place by means of an intramolecular metal-assisted [4+2] cycloaddition. The beneficial role of microwave activation has been studied. It is concluded that microwave irradiation can decrease the catalytic induction period through thermal effects and can also increase the triplet lifetime and promote the reaction, thus improving the final yield.