**Appendix A.**

The fitting procedures performed are reported in the following, by outlining the expression used and showing an example of result and the corresponding error.

#### *Appendix A.1. Fitting of Raman Signals*

The Raman spectra have been analyzed with Matlab, using a Lorentz fitting, to obtain the Raman spectrum parameters, such as frequency peak position, width, intensity and area of the peak. The fitting of a spectrum, collected under excitation at 514.5 nm, is reported in Figure A1, and the corresponding parameters obtained from the fitting are reported in Table A1. The goodness of the Lorentz fitting is evaluated with the R<sup>2</sup> parameter, known as the coefficient of determination in statistics, it is calculated from the sum of squared errors. It indicates the proportionate amount of variation in the response variable explained by the independent variables in the model. The larger it is, the more variability is explained by the model.


**Figure A1.** Experimental data collected at *λexc* = 514.5 nm (open circles) fitted with a Lorentzian curve (red line).

#### *Appendix A.2. Fitting of Experimental Anti-Stokes/Stokes Ratios as Function of Temperature*

The calibration coefficients have been obtained by fitting anti-Stokes over Stokes ratio data, at each excitation wavelength, using the equation:

$$\rho = \mathcal{C} \cdot \frac{\left(\upsilon\_0 + \upsilon\right)^3}{\left(\upsilon\_0 - \upsilon\right)^3} \exp\left(-\frac{h\upsilon}{kT}\right),$$

We substitute *v*0 = 5.83·10<sup>14</sup> *s*<sup>−</sup><sup>1</sup> as *λexc* = 514.5 nm , *v* = 4.29·10<sup>12</sup> *s*<sup>−</sup><sup>1</sup> (frequency of the 143.0 cm<sup>−</sup><sup>1</sup> Raman mode), and the values of the Planck and Boltzmann constants. Temperatures are those imposed by the temperature-controlled stage. *C* is left as a free parameter. The value, obtained with data reported in Figure A2, *C* = 0.961 ± 0.006 is the calibration constant for the 143 cm<sup>−</sup><sup>1</sup> Raman mode and *λexc* = 514.5 nm). The value of the R<sup>2</sup> for this fitting is 0.95.

#### *Appendix A.3. Theoretical Anti-Stokes/Stokes Ratio Behavior as Function of Temperature*

The determination of the local temperature using the strength of a Raman band at the Stokes and anti-Stokes position is based on the Boltzmann distribution of the ground and first excited state populations. At room temperature a significant difference between the Stokes and anti-Stokes signal strengths are expected, since the population of the ground state will be higher than that of the excited one, for an oscillator with energy proportional to 140 cm<sup>−</sup>1, as can be observed from Figure 2. It is also evident that the higher the energy of the vibrational mode is, the lower the population of the excited state and therefore the weaker the signal strength of the anti-Stokes Raman band will be. At increasing temperature, the population of the excited state increases, thus increasing the intensity of the anti-Stokes band and decreasing the intensity of the corresponding Stokes band. The dependence of this variations is strictly related to the population distribution, related to the Boltzmann distribution, which consider an exponential dependence with temperature.

Figure A3 reports the behavior of the Stokes over anti-Stokes area ratio of the Anatase Raman modes as a function of the temperature, only on a large temperature range the exponential behavior is evident, while by considering the small range the behavior seems to be linear, but it is necessary to consider an exponential dependence due to the underlined process.

**Figure A3.** Theoretical anti-Stokes/Stokes ratio evaluated at λexc = 514.5 nm, for all the four Raman modes of titanium dioxide, in a temperature range 0–2200 K (**a**) and in the range of interest (**b**).

Theoretical models predict a direct dependence of the Stokes and anti-Stokes Raman intensity on the temperature, but experimental data show a direct correlation with temperature of the anti-Stokes/Stokes ratio. This fact, already observed in literature [10,45–48], can be ascribed also to small variations of experimental parameters, like the intensity of the laser, the effective focal volume, linked to the position of the focus on the sample, to the inhomogeneity of the sample, which can lead to a number of different active molecules in the focal volume. All these experimental parameters will influence the absolute intensity of the Raman bands. By performing the ratio between anti-Stokes and Stokes bands a sort of internal normalization is obtained.
