Quantum thermal states are ubiquitous in physics and quantum algorithms. They serve as the state of the system at a given temperature and are therefore useful primitives in simulating quantum chemistry and condensed matter. It is still an open question to develop a complete theory for how quantum systems approach thermal equilibrium and an open problem to develop algorithms for preparing these states on digital quantum computers. In our talk we will demonstrate how an extension of the theory of Repeated Interactions can be used to build completely analyzable algorithms for quantum computers. We will present an introduction to our algorithm, a brief analysis on the harmonic oscillator, and finally sketch theoretic and numeric results for generic systems.