  We investigate the saturation level of hydromagnetic turbulence driven by the
magnetorotational instability in the case of vanishing net flux. Motivated by a
recent paper of Bodo, Cattaneo, Mignone, & Rossi, we here focus on the case of
a non-isothermal equation of state with constant thermal diffusivity. The
central aim of the paper is to complement the previous result with closure
parameters for mean-field dynamo models, and to test the hypothesis that the
dynamo is affected by the mode of heat transport. We perform computer
simulations of local shearing-box models of stratified accretion disks with
approximate treatment of radiative heat transport, which is modeled via thermal
conduction. We study the effect of varying the (constant) thermal diffusivity,
and apply different vertical boundary conditions. In the case of impenetrable
vertical boundaries, we confirm the transition from mainly conductive to mainly
convective vertical heat transport below a critical thermal diffusivity. This
transition is however much less dramatic when more natural outflow boundary
conditions are applied. Similarly, the enhancement of magnetic activity in this
case is less pronounced. Nevertheless, heating via turbulent dissipation
determines the thermodynamic structure of accretion disks, and clearly affects
the properties of the related dynamo. This effect may however have been
overestimated in previous work, and a careful study of the role played by
boundaries will be required.
