Micro- and nanoswimmers are a fast emerging concept that changes how colloidal and biological systems interact. They can support drug delivery vehicles, assist in crossing biological barriers, or improve diagnostics. We report microswimmers that employ collagen, a major extracellular matrix (ECM) constituent, as fuel and that have the ability to deliver heat via incorporated magnetic nanoparticles when exposed to an alternating magnetic field (AMF). Their assembly and heating properties are outlined followed by the assessment of their calcium-triggered mobility in aqueous solution and collagen gels. It is illustrated that the swimmers in collagen gel in the presence of a steep calcium gradient exhibit fast and directed mobility. The experimental data are supported with theoretical considerations. Finally, the successful penetration of the swimmers into 3D cell spheroids is shown, and upon exposure to an AMF, the cell viability is impaired due to the locally delivered heat. This report illustrates an opportunity to employ swimmers to enhance tissue penetration for cargo delivery via controlled interaction with the ECM.