We use the path integral Monte Carlo method to investigate the interplay be
tween shell effects and electron correlations in single quantum dots with u
p to 12 electrons. By use of an energy estimator based on the hypervirial t
heorem of Hirschfelder we study the energy contributions of different inter
action terms in detail. We discuss under which conditions the total spin of
the electrons is given by Hund's rule, and the temperature dependence of t
he crystallization effects.