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, 1s) 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.