Collagen fibrils form extracellular networks that regulate cell functions and provide mechanical strength to tissues. Collagen fibrillogenesis is an entropy-driven process promoted by warming and reversed by cooling. Here, we investigate the influence of noncovalent interactions mediated by the collagen triple helix on fibril stability. We measure the kinetics of cold-induced disassembly of fibrils formed from purified collagen I using turbimetry, probe the fibril morphology by atomic force microscopy, and measure the network connectivity by confocal microscopy and rheometry. We demonstrate that collagen fibrils disassemble by subunit release from their sides as well as their ends, with complex kinetics involving an initial fast release followed by a slow release. Surprisingly, the fibrils are gradually stabilized over time, leading to thermal memory. This dynamic stabilization may reflect structural plasticity of the collagen fibrils arising from their complex structure. In addition, we propose that the polymeric nature of collagen monomers may lead to slow kinetics of subunit desorption from the fibril surface. Dynamic stabilization of fibrils may be relevant in the initial stages of collagen assembly during embryogenesis, fibrosis, and wound healing. Moreover, our results are relevant for tissue repair and drug delivery applications, where it is crucial to control fibril stability.