  We study numerically the onset of convection in Rotating Rayleigh-B\'enard
convection in horizontally confined geometries of aspect ratio $2$ with the
walls held at fixed temperatures. We show that this arrangement is
unconditionally unstable to flow that takes the form of wall-adjacent
convection rolls. For wall temperatures close to the temperatures of the upper
or lower boundaries, we show that the base state undergoes a Hopf bifurcation
to a state comprised of spatio-temporal oscillations--`wall modes'--precessing
in a retrograde direction. We show that the velocity boundary conditions at the
upper and lower boundaries are crucial to the formation and propagation of the
wall modes: asymmetric velocity boundary conditions at the upper and lower
boundaries can lead to prograde wall modes, while stress-free boundary
conditions at both walls can lead to wall modes that have no preferred
direction of propagation.
