Although several force application concepts are known that can be used to deform shape memory polymers (SMPs) within the scope of programming, controlled deformation is challenging in the case of samples with a cylinder-like shape, which need to be homogeneously compressed starting from the lateral surface. To solve this problem, this contribution follows a material approach that takes advantage of four-dimensional (4D) printing. Fused filament fabrication (FFF) was used as an additive manufacturing (AM) technique to produce a thermoresponsive tool in a cylindrical shape from a polyether urethane (PEU) having a glass transition temperature (Tg) close to 55 °C, as determined by differential scanning calorimetry (DSC). Once it was 4D-printed, a sample of laser cut polyester urethane urea (PEUU) foam with a cylindrical wall was placed inside of it. Subsequent heating to 75 °C and keeping that temperature constant for 15 min resulted in the compression of the foam, because the internal stresses of the PEU were transferred to the PEUU, whose soft segments were completely molten at 65 °C as verified by DSC. Upon cooling to −15 °C and thus below the offset temperature of the soft segment crystallization transition of the PEUU, the foam was fixed in its new shape. After 900 days of storage at temperatures close to 23 °C, the foam recovered its original shape upon reheating to 75 °C. In another experiment, a 4D-printed cylinder was put into hibernation for 900 days before its thermoresponsiveness was investigated. In the future, 4D-printed tools may be produced in many geometries, which fit well to the shapes of the SMPs to be programmed. Beyond programming SMP foams, transferring the forces released by 4D-printed tools to other programmable materials can further expand technical possibilities.