A simple model for drift-thermal instability-induced turbulence is derived and studied both analytically and numerically. Both nonlocal, nonlinear analytical calculations and three-dimensional computations are used. Potential and temperature fluctuation levels and radial correlation lengths are calculated and compared to numerical results. The saturation mechanism and the role of a fluctuation-generated shear flow are elucidated. The numerical calculations are used to obtain spectra and correlation lengths. A detailed comparison of analytical and numerical results is given.