A time-dependent “convective diffusion” algorithm for convective transport in the mixing-length framework has been coupled for the first time with a self-consistent full evolutionary computation, in order to investigate theoretically the creation of superrich lithium stars on the asymptotic giant branch. For intermediate mass stars in the mass range from 4 to 7 M⊙ with both Population I and II compositions, hot bottom burning in the convective envelope was found, with maximum temperatures Tce at the base of the convective envelope ranging from 20 to 100 million K, depending on stellar mass and mass loss rates. For Tce ≥ 40 million K, lithium-rich giants were produced (with log ε(7Li) ≳ 1, i.e., above the normal observed range in giants). For Tce ≥ 50 million K, superrich lithium giants were created, with log ε(7Li) ≳ 3 (i.e., larger than the present cosmic7Li abundance).