In one-well geothermal plant, the mass flow of the geothermal fluid between the aquifer and the heat exchanger is supplied only by one well. It is universally acknowledged that this type of plant has some thermal and fluid dynamic limits and, therefore, they were proposed only for low and medium thermal applications; however simple models are lacking to explain and correctly evaluate these limits. The fundamentals of a lumped parameter model of the thermal and fluid dynamic phenomena giving rise to heat flow limits were explained by Carotenuto et al. (A. Carotenuto, C. Casarosa, M. Dell'Isola, L. Martorano, An aquifer-well thermal and fluid dynamic model for downhole heat exchangers with a natural convection promoter, Int. J. Heat Mass Transfer 40(18) (1997) 4461-4472; A. Carotenuto, C. Casarosa, Modello a Parametri Concentrati dei Limiti Operativi di Impianti Geotermici a Pozzo Unico. Parte I: Elementi Generali, 53 degrees Congresso Nazionale ATI, Firenze, vol. I, 1998, pp. 557-570). In this paper, the model is completely developed for natural convection plant in which the geothermal fluid flow between aquifer and well is provided only by the temperature drop occurring in the heat exchanger. The model is applied to this type of plant taking into consideration, whether: (i) a natural convection promoter is present and (ii) downhole heat exchangers or geothermal convectors (GTCs) are used. In particular, for GTCs, the model is successfully applied to evaluate the experimental data obtained by the authors in previous experimental tests.