We investigate the process of formation and subsequent evolution of prominence plasma in a filament channel and its overlying arcade. We construct a three-dimensional time-dependent model of an intermediate quiescent prominence suitable to be compared with observations. We combine the magnetic field structure of a three-dimensional sheared double arcade with one-dimensional independent simulations of many selected flux tubes, in which the thermal nonequilibrium process governs the plasma evolution. We have found that the condensations in the corona can be divided into two populations: threads and blobs. Threads are massive condensations that linger in the flux tube dips. Blobs are ubiquitous small condensations that are produced throughout the filament and overlying arcade magnetic structure, and rapidly fall to the chromosphere. The threads are the principal contributors to the total mass, whereas the blob contribution is small. The total prominence mass is in agreement with observations, assuming reasonable filling factors of order 0.001 and a fixed number of threads. The motion of the threads is basically horizontal, while blobs move in all directions along the field. We have generated synthetic images of the whole structure in an Hα proxy and in two EUV channels of the Atmospheric Imaging Assembly instrument on board Solar Dynamics Observatory, thus showing the plasma at cool, warm, and hot temperatures. The predicted differential emission measure of our system agrees very well with observations in the temperature range log T = 4.6-5.7. We conclude that the sheared-arcade magnetic structure and plasma behavior driven by thermal nonequilibrium fit the abundant observational evidence well for typical intermediate prominences.