Thermal management of stretchable and wearable electronic devices is an important issue in enhancing performance, reliability, and human thermal comfort. Here, we constructed a unique experimental setup which investigated the strain-dependent thermal conductivity. The thermal conductivity of flower-shaped silver nanoparticle (silver nanoflower)-polyurethane (Ag-PU) composite fibers was systematically investigated as a function of strain. The strain-dependent temperature distribution of the Joule-heated fiber was measured using an infrared camera, and the thermal conductivity was obtained from the 1-dimensional Fourier's conduction model. There was a monotonic decrease in both lattice and electronic thermal conductivity with stretching at 25 °C. However, there was an initial increase in lattice and total thermal conductivity in the low strain region (<10%), when the fiber was stretched at 45 °C, although the electronic thermal conductivity decreased monotonically. The softening of the polymer at increased temperatures enhanced Poisson's ratio. Resultantly, the fiber cross-sectional area and radial-direction inter-particle distance between silver nanoflowers decreased. This could increase the thermal transport in conductive fibers by modulating the interfaces between silver nanoflowers and polyurethane. A further stretching decreased the lattice thermal conductivity due to the significantly increased axial distance between silver nanoflowers and the decreased filler fraction. The weft-knitted fabric also demonstrated an increased thermal conductance in the low strain region (≤30%) at 45 °C.