In order to investigate Last Glacial Maximum and future climate, we “precalibrate” the intermediate complexity model GENIE-1 by applying a rejection sampling approach to deterministic emulations of the model. We develop ~1,000 parameter sets which reproduce the main features of modern climate, but not precise observations. This allows a wide range of large-scale feedback response strengths which generally encompass the range of GCM behaviour. We build a deterministic emulator of climate sensitivity and quantify the contributions of atmospheric (±0.93°C, 1σ) vegetation (±0.32°C), ocean (±0.24°C) and sea–ice (±0.14°C) parameterisations to the total uncertainty. We then perform an LGM-constrained Bayesian calibration, incorporating data-driven priors and formally accounting for structural error. We estimate climate sensitivity as likely (66% confidence) to lie in the range 2.6–4.4°C, with a peak probability at 3.6°C. We estimate LGM cooling likely to lie in the range 5.3–7.5°C, with a peak probability at 6.2°C. In addition to estimates of global temperature change, we apply our ensembles to derive LGM and 2xCO2 probability distributions for land carbon storage, Atlantic overturning and sea–ice coverage. Notably, under 2xCO2 we calculate a probability of 37% that equilibrium terrestrial carbon storage is reduced from modern values, so the land sink has become a net source of atmospheric CO2.