There has been a strong and recent research activity to obtain tunable wrinkling patterns in film/substrate systems, which proposes to use geometric curvature as a control parameter. This paper studies core-shell cylindrical systems under thermal loads, with the aim to describe possible wrinkling modes, bifurcation diagrams and dimensionless parameters influencing the response of the system. In the companion case of axially compressed core-shell cylinders, it was established that instability modes can be axisymmetric or diamond-like, the post-buckling response of the system is governed by a single dimensionless parameter C s , and the bifurcation becomes supercritical for a sufficiently stiff core. In the present case of cylindrical core-shells subjected to thermal loading, one finds quite different buckling patterns, named churro-like modes that are characterized by a fast undulation in the circumferential direction. There exists another curvature-related influencing parameter C t , and a subcritical to supercritical bifurcation transition is observed when the core stiffness increases. The problem is analyzed both theoretically and numerically based on finite element calculations. Lastly, the obtained instability modes remain about the same as in pure shell structures, the main difference being the stabilization of the post-bifurcation behavior.