  To understand solar and stellar dynamos combining local and global numerical
modelling with long-term observations is a challenging task: even with state of
the art computational methods and resources, the stellar parameter regime
remains unattainable. Our goal is to relax some approximations, in order to
simulate more realistic systems, and try to connect the results with
theoretical predictions and state-of-the-art observations. We present here the
first test-field measurements from our higher-resolution runs with improved
heat conduction description. They indicate significant changes in the profiles
of the most crucial inductive effect related to solar and stellar dynamo
mechanisms. Higher resolution runs, currently undertaken, will bring us into an
even more turbulent regime, in which we will be able to study, for the first
time, the interaction of small- and large-scale dynamos in a quantitative way.
