  Self-propelling active matter relies on the conversion of energy from the
undirected, nanoscopic scale to directed, macroscopic motion. One of the
challenges in the design of synthetic active matter lies in the control of
dynamic states, or motility gaits. Here, we present an experimental system of
self-propelling droplets with thermally controllable and reversible dynamic
states, from unsteady over meandering to persistent to arrested motion. These
states depend on the P\'eclet number of the molecular process powering the
motion, which we can tune by using a temperature sensitive mixture of
surfactants as a fuel medium. We quantify the droplet dynamics by analysing
flow and chemical fields for the individual states, comparing them to canonical
models for autophoretic particles. In the context of these models, we
experimentally observe, in situ, the fundamental first broken symmetry that
translates an isotropic, immotile base state to self-propelled motility.
