  We give a detailed description of the implementation of a Molmer-Sorensen
gate entangling two Ca+ ions using a bichromatic laser beam near-resonant with
a quadrupole transition. By amplitude pulse shaping and compensation of
AC-Stark shifts we achieve a fast gate operation without compromising the error
rate. Subjecting different input states to concatenations of up to 21
individual gate operations reveals Bell state fidelities above 0.80. In
principle, the entangling gate does not require ground state cooling of the
ions as long as the Lamb-Dicke criterion is fulfilled. We present the first
experimental evidence for this claim and create Bell states with a fidelity of
0.974(1) for ions in a thermal state of motion with a mean phonon number of
<n>=20(2) in the mode coupling to the ions' internal states.
