The Tipping Points Modelling Intercomparison Project (TIPMIP) samples common rates and levels of global warming (GWL) across physical, biophysical and biogeochemical domains, rather than a common calendar year or CO₂ level. In the Tier 1 experiments, emission-driven Earth system models (ESM) are forced by a constant CO₂-emission rate intended to yield 2 °C of warming per century. This ramp-up phase is followed by emission cessation (zero-emission runs) at selected GWLs, from which ramp-down runs are branched 50 years later using the negative of the ramp-up emission rate. A common rate of global warming is targeted in the ramp-up phase, but realised rates deviate from this target, particularly at higher levels of warming, and diverge further in the ramp-down phase, where the link between negative CO₂ emissions and global temperature is less established; as a result, equal calendar years do not correspond to equal GWLs across models. A standardised mapping from model years to a temperature axis is therefore needed for diagnostics to be analysed and compared consistently as a function of GWL. We propose such a mapping here. We define GWL as the global-mean near-surface air temperature (GMSAT) anomaly relative to each model's own pre-industrial control, taken as a 31-year window centred on the branch year, the point at which the ramp-up run diverges from the pre-industrial control. The method maps any diagnostic from calendar time onto a common GWL axis in three steps: computing the warming anomaly, smoothing and enforcing monotonicity, and inverting the result to express any diagnostic against GWL at native resolution or on a shared grid. The inversion is applied to the ramp-up leg and to both Tier 1 ramp-down legs, from the zero emission runs started at 2 and 4 °C GWL. Applying the method to nine available TIPMIP ESMs, we show the mapping is robust to its principal methodological choices, with baseline and smoothing-window sensitivities both under 0.1 °C, so results can be reported at 0.1 °C resolution regardless of these choices. We publish the resulting GWL axes for each model and leg as a versioned, provenance-stamped data product, together with an open-source Python implementation, so downstream analyses can share one common coordinate transformation rather than each constructing their own.