Geologist here -- happy to answer any questions about this! The underlying paper [1] and the older one it builds on [2] are both open access. The rj-MCMC for the time-temperature inversion used an existing program from the thermochron community, but we made most of the figures in Julia.
[1] https://doi.org/10.1073/pnas.2118682119
[2] https://doi.org/10.1073/pnas.1804350116