**Algorithm 3** Calculation of T.

```
Require: n, m, Ea, A0, Tmax, T0,α0, dt
  T0 = T0
  α0 = α0
  while αi ≤ 1 do
    αi+1 = A0 exp(−Ea/RTi)αm
                                i (1 − αi)n ∗ dt + αi
    Ti+1 = ETot
            Ctot (αi+1 − αi) + Ti
  end while
```
**Figure 10.** Simulation. (**a**) Simulation of the different kinetics for a time of simulation corresponding to the tests. Comparison with the test data. (**b**) Simulation of the different kinetics considering that no other reaction occurs until the end.

## **5. Conclusions**

Thanks to the ARC tests realised on cells aged by different processes, we have shown that (*m*, *l*) parameters must be chosen carefully. Indeed these parameters vary according to ageing and what the cell experienced.

The values of (*m*, *l*) impact the energy of activation and the pre-exponential factor. The transition state theory shows that energy of activation and pre-exponential factor cannot be considered constant. They vary according to the history of the cell. First, the ageing changes the morphology of the cell and consequently the reaction that will be produced. Secondly, the rise in the temperature will change the equilibrium of the reaction, therefore the energy required to trigger the reaction will not be the same.

Once all the kinetic parameters are calculated, simulations can be used to reproduce the rise in temperature. Simulations confirm that the kinetic parameters must be estimated at different temperatures but with constant kinetics. One reaction can impose its kinetics but a new reaction can take over and in turn impose its own kinetics. In this case all the kinetic parameters must be re-evaluated, for each range of temperatures.

Simulations have exposed another problem: some cells are considered more stable thermally because the reaction starts at a higher temperature. However, in this case, the reaction will be realised faster. Other cells have a lower temperature onset but the reaction will be slower, which gives time to find solutions to a thermal runaway. Should we focus on stability in order to minimise the risk of thermal runaway, or should we focus on the time response in case of thermal runaway?

**Author Contributions:** Writing, modelling, and simulation: M.G.; post-mortem analysis and cell performance measurement (ARC, cycling, ...): P.K.; EIS and post-mortem analysis: S.G.; validation and supervision: O.R.; methodology and supervision: P.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
