C2 is favoured by kinetic control; C1 is favoured by thermodynamic control. Starting from the central reactant well, the path towards C2 has the smaller activation barrier, so it normally forms faster at low temperature or short reaction time, assuming comparable prefactors. C1 lies lower in energy and is the more stable product on the drawn energy scale.
Raising temperature can make the larger barrier accessible and permit equilibration through reverse reactions. If products interconvert and entropy contributions do not reverse the energy ordering, the equilibrium mixture then favours C1. It would be incorrect to say that high temperature alone guarantees C1: an irreversible reaction may remain kinetically controlled, and the figure does not provide the full temperature-dependent free energies. The useful distinction is rate selection before equilibration versus relative free energy after equilibration.