Our technologies have never ceased to evolve, allowing our lineage to expand its habitat all over the Earth, and even to explore space. This phenomenon, called cumulative technological culture (CTC), has been studied extensively, notably using mathematical and computational models. However, the cognitive capacities needed for the emergence and maintenance of CTC remain largely unknown. In the literature, the focus is put on the distinctive ability of humans to imitate, with an emphasis on our unique social skills underlying it, namely theory of mind (ToM). A recent alternative view, called the technical-reasoning hypothesis, proposes that our unique ability to understand the physical world (i.e., technical reasoning; TR) might also play a critical role in CTC. Here, we propose a simple model, based on the micro-society paradigm, that integrates these two hypotheses. The model is composed of a simple environment with only one technology that is transmitted between generations of individuals. These individuals have two cognitive skills: ToM and TR, and can learn in different social-learning conditions to improve the technology. The results of the model show that TR can support both the transmission of information and the modification of the technology, and that ToM is not necessary for the emergence of CTC although it allows a faster growth rate.