  Different scaling behavior has been reported in various shell models proposed
for turbulent thermal convection. In this paper, we show that buoyancy is not
always relevant to the statistical properties of these shell models even though
there is an explicit coupling between velocity and temperature in the equations
of motion. When buoyancy is relevant (irrelevant) to the statistical
properties, the scaling behavior is Bolgiano-Obukhov (Kolmogorov) plus
intermittency corrections. We show that the intermittency corrections of
temperature could be solely attributed to fluctuations in the entropy transfer
rate when buoyancy is relevant but due to fluctuations in both energy and
entropy transfer rates when buoyancy is irrelevant. This difference can be used
as a criterion to distinguish whether temperature is behaving as an active or a
passive scalar.
