At hemispheric scale, the surface temperature is strongly influenced by the 28 variations of the natural (solar and volcanic) and anthropogenic (land-use, sulphate aerosols, greenhouse gas concentrations) forcings. By contrast, at regional scale, the internal variability, which is purely due to the internal dynamics of the climate system, can mask the forced response. As a consequence, before the 20th century, cold or warm periods are rarely global, homogenous phenomena. Furthermore, the response to the forcing could be associated with changes in the frequency of some modes of variability. This interplay between the response of the climate system to the various forcings and internal variability makes model-data comparison a complex task for the last millennia. In this framework, simulations in which the model is forced to follow the observations using a data assimilation technique could be very useful. Their goal is to extract the information on the forced and internal variability contained in both the proxy records and model results using a single procedure.