  We present numerical simulations, using two complementary setups, of rotating
Boussinesq thermal convection in a three-dimensional Cartesian geometry with
misaligned gravity and rotation vectors. This model represents a small region
at a non-polar latitude in the convection zone of a star or planet. We
investigate the effects of rotation on the bulk properties of convection at
different latitudes, focusing on determining the relation between the heat flux
and temperature gradient. We show that our results may be interpreted using
rotating mixing length theory (RMLT). The simplest version of RMLT (due to
Stevenson) considers the single mode that transports the most heat. This works
reasonably well in explaining our results, but there is a systematic departure
from these predictions (up to approximately $30\%$ in the temperature gradient)
at mid-latitudes. We develop a more detailed treatment of RMLT that includes
the transport afforded by multiple modes, and we show that this accounts for
most of the systematic differences. We also show that convectively-generated
zonal flows and meridional circulations are produced in our simulations, and
that their properties depend strongly on the dimensions of the box. These flows
also affect the heat transport, contributing to departures from RMLT at some
latitudes. However, we find the theoretical predictions of the multi-mode
theory for the mid-layer temperature gradient, the root-mean-square (RMS)
vertical velocity, the RMS temperature fluctuation, and the spatial spectrum of
the heat transport at different latitudes, are all in reasonably good agreement
with our numerical results when zonal flows are small.
