  Modelling of the weak lensing of the CMB will be crucial to obtain correct
cosmological parameter constraints from forthcoming precision CMB anisotropy
observations. The lensing affects the power spectrum as well as inducing
non-Gaussianities. We discuss the simulation of full sky CMB maps in the weak
lensing approximation and describe a fast numerical code. The series expansion
in the deflection angle cannot be used to simulate accurate CMB maps, so a
pixel remapping must be used. For parameter estimation accounting for the
change in the power spectrum but assuming Gaussianity is sufficient to obtain
accurate results up to Planck sensitivity using current tools. A fuller
analysis may be required to obtain accurate error estimates and for more
sensitive observations. We demonstrate a simple full sky simulation and
subsequent parameter estimation at Planck-like sensitivity. The lensed CMB
simulation and parameter estimation codes are publicly available.
