Résumé : In a warming world, glaciers and ice sheets have an increasingly large influence on the environment, particularly through their contribution to sea level rise. Their response to anthropogenic climate change, in addition to natural variability, has a critical impact on dependent populations and will be key to predict future climates. Understanding the past natural transitions is also important as if the natural variability of the climate system is not well understood, we stand little change of accurately predicting future climate changes, especially in the context of rapid global warming. Ice cores represent the best time capsules for the recovery of paleo-climate informations. For that, the recovery of a suitable 1.5 million-year-old ice core in Antarctica is fundamental to better understand the natural climate reorganisation which occurred between 0.9 and 1.2 Ma. Constraining the englacial and basal temperature evolution of glaciers and ice sheets through time is the first step in understanding their temporal stability and therefore potential impacts on climate. Furthermore, obtaining the best constraints on basal conditions is essential as such million-year-old ice will be located very near to the bedrock, where the thermal regime has the strongest impact. However, measurements of current englacial and basal temperature have only been obtained at a few drill sites for glaciers and ice sheets. We must therefore turn to thermodynamical models to provide theoretical and statistical constraints on governing thermal processes. Thermodynamical models rely on a suite of governing equations, which we describe in this thesis. Our first study area is the McCall glacier, in Alaska (USA), where we show that the glacier cooled down in the warming climate of the last 50 years using a 1D thermodynamical model. We calculate the present-day englacial temperature distribution using recently acquired data in the form of englacial temperature measurements and radio-echo sounding surveys of the glacier. We show the important of absence of latent heat release due to the refreezing of meltwater inside an active surface layer and reconstruct the last 50 years of equilibrium line altitude (ELA) elevation changes. In the context of Beyond Epica Oldest Ice, a European project aimed at recovering a 1.5 million year-old ice core, we propose for the first time a map of the location of adequate drilling sites for the entire Antarctic Ice Sheet. We use a 3D thermomechanical model to calculate a new basal temperature map of the Antarctic Ice Sheet, as well as a 1D thermodynamical model to constrain the poorly known geothermal heat flux (GHF). These combined model runs use the latest acquired data sets for the GHF, ice flow velocity, ice thickness and subglacial lakes. In order to take into account 2 Ma of Antarctic climate history, we use a transient 1D thermodynamical model to provide constraints on GHF by calculating the maximum value of GHF allowed to keep frozen basal conditions everywhere underneath the ice sheet. These values are then statistically compared to published GHF data sets to propose a probabilistic map of frozen and thawed bedrock locations. This transient model uses high spatial resolution radar data acquired over the Dome Fuji and Dome C regions to examine their likelihood of having preserved 1.5-million-year ice. We define a number of important criteria such as GHF, bedrock variability, ice thickness and other parameter values for Oldest Ice survival. We anticipate that our methods will be highly relevant for Oldest Ice prospection in other areas of the ice sheet that so far remain little or un-surveyed, as well as for the thermal modelling of other glaciers and ice sheets, and in particular, of the Greenland Ice Sheet.