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In this work, we demonstrate the usability of a fully-2D-material based device consisting of MoS₂/WSe₂ heterojunction encapsulated by hBN and contacted by graphene as temperature sensor for linear temperature measurement at cryogenic temperatures. More precisely, temperatures in the range of 10 K up to 300 K were applied to the device while recording the <italic>I-V</italic> characteristics. In contrast to the classical expectation, the main current flows through the device when it is reversely biased. We ascribe this to a combination of drift-diffusion and band-to-band tunneling, while for very low temperatures (T <inline-formula> <tex-math notation="LaTeX">$ &lt; $ </tex-math></inline-formula> 100 K), variable-range hopping or trap-assisted tunneling seems dominant. In case of forward bias, the Schottky contact on the WSe₂-anode hinders the charge transport in the voltage range of interest. Additionally, we obtained the activation energy of the saturation current in reverse direction in an Arrhenius diagram. Depending on the bias level, it varies between 100 meV and 300 meV, which may be related to the energy barrier caused by interface traps, generation centers between both semiconducting 2D materials, and the band-to-band tunneling. Furthermore, we investigated the temperature-sensor performance by applying a constant current to the device and measuring the voltage drop at different temperatures. In the range of 40 K up to 300 K, the sensitivity of the sensor is <inline-formula> <tex-math notation="LaTeX">$\sim 2$ </tex-math></inline-formula> mV/K, which is comparable to Si devices, while the linearity is still lower <inline-formula> <tex-math notation="LaTeX">$(R^{2}~\sim ~0.94$ </tex-math></inline-formula>). On the other hand, the demonstrated device consists only of 2D materials and is, thus, substrate independent, very thin, and can potentially be fabricated on a fully flexible substrate in a low-cost process.