Earth is warming and sea levels are rising as land-based ice is lost to melt, and oceans expand due to accumulation of heat. The pace of ice loss and steric expansion is linked to the intensity of warming. How much faster sea level will rise as climate warms is, however, highly uncertain and difficult to model. Here, we quantify the transient sea level sensitivity (TSLS) of the sea level budget in both models and observations. Models show little change in sensitivity between the first and second half of the 21^st century for most contributors. The exception is glaciers and ice caps (GIC) that have a greater sensitivity pre-2050 (2.8±0.4 mm/yr/K) compared to later (0.7±0.1 mm/yr/K). We attribute this change to the short response time of glaciers and their changing area over time. Model sensitivities of steric expansion (1.5±0.2 mm/yr/K), and Greenland Ice Sheet mass loss (0.8±0.2 mm/yr/K) are greater than, but still compatible with, corresponding estimates from historical data (1.4±0.5 mm/yr/K and 0.5±0.1 mm/yr/K). Antarctic Ice Sheet (AIS) models tends to show lower rates of sea level rise with warming (‑0.0±0.3 mm/yr/K) in contrast to historical estimates (0.4±0.2 mm/yr/K). This apparent low bias in AIS sensitivity is only partly able to account for a similar low bias identified in the sensitivity of GMSL excluding GIC (3.2±0.5 mm/yr/K vs 2.2±0.4 mm/yr/K). The balance temperature, where sea level rise is zero, lies close to the pre-industrial value, implying that sea level rise can only be mitigated by substantial global cooling.