The evolution of a star forming molecular cloud depends critically on the thermodynamic processes, which determine the temperature, and hence the pressure, of the gas, i.e. heating, cooling, chemistry and radiation transport. These processes play a key role in determining the overall efficiency of star formation, the stellar initial mass function, the patterns of clustering, the binary statistics, the masses and lifetimes of accretion discs, and the external appearance of star forming clouds.The aim of this proposal is to explore the influence of thermodynamic processes on star formation by developing state-of-the-art algorithms to model them, and then combining these algorithms with high-resolution numerical simulations of star formation, using initial and boundary conditions informed by the latest observations. This in turn will allow us to determine how star formation depends on environmental factors like epoch, metallicity, background radiation field, level of turbulence, and feedback.This has implications beyond contemporary, local star formation, since observers are now able to observe star formation in more extreme environments like starbursts, and high-redshift merging proto-galaxies, and it is important to know and explain what systematic differences there may be between the patterns of star formation in these different environments.