It is difficult to answer this general question since it is not clear what exactly you mean with "ultrafast spectroscopy"? Just for illustration:

- If you mean optical emission spectroscopy generated by laser ablation with ultrashort laser pulses (Laser-induced breakdow spectroscopy, LIBS), then you may estimate the electron temperature in the (low density) laser ablation plasma from intensity ratios of the discrete atomic optical emission lines involved, for a good book you may check H.R. Griem "Principles of Plasma Spectroscopy", Cambride University Press.

Article Principles of Plasma Spectroscopy

- On the other hand, if you refer to X-ray emission generated from a hot laser-induced (high density) electron plasma, you may analyze the spectral distribution of the emitted hard X--ray photons in the continuous (Bremsstrahlungs)spectrum and fit it to a Maxwellian distribution. For an example see Article X-ray emission as a potential hazard during ultrashort pulse...

and check the references therein.

These two examples describe two totally different variants of ultrafast spectroscopy and there are many more things hidden behind the tag "ultrafast spectroscopy", e.g. ultrafast spectroscopic experiments with additionaly time resolution or with imaging capabilities. I think it would help to further specify what exactly you are looking for...