Abstract This chapter addresses an inverse problem in glaciology, namely how to infer a climatic scenario (i.e. how to reconstruct past polar temperature) from ice volume records. Ice volume observations are available from oceanic records, giving information about sea level, and therefore about the amount of water stored in ice sheets, ice caps, and glaciers. The link between the climatic scenario and the ice sheet volume is complex. The temperature affects the ice mass budget (accumulating minus melting ice). Then, the ice mass budget is a key factor in ice dynamics, which is quite complex in itself (non-Newtonian fluid and nonlinear rheology). The few previous studies of this subject have used fairly simple inverse methods. The idea of the approach described in this chapter is to explore, with idealized twin experiments, the ability of the adjoint method to solve the inverse problem of reconstructing past temperature given all available observations.