Thermal phenomena like heat transfer can arise in systems that are deterministic at the microscopic level. Indeed, at the time of Boltzmann (pre quantum) one of the major questions is how to go from deterministic but complex & unpredictable classical particle dynamics to continuum models like the heat equation. Kinetic theory is one piece of that bridge between scales.
In more recent times these questions are still studied, e.g., within mathematical physics / ergodic theory circles. Look up "Lorentz gas", "Fourier law", etc. Usually to get anything interesting one needs to hook these systems up to "reservoirs", which are usually stochastic. In principle one could replace the reservoirs by another large, chaotic classical system but that makes the mathematical questions too hard, and having some randomness in a small corner of the system and studying how its influence spreads is still very challenging but more tractable.
In more recent times these questions are still studied, e.g., within mathematical physics / ergodic theory circles. Look up "Lorentz gas", "Fourier law", etc. Usually to get anything interesting one needs to hook these systems up to "reservoirs", which are usually stochastic. In principle one could replace the reservoirs by another large, chaotic classical system but that makes the mathematical questions too hard, and having some randomness in a small corner of the system and studying how its influence spreads is still very challenging but more tractable.