The rising complexity of cutting-edge cryogenic systems is currently imposing challenging technical constraints to the monitoring of ultra-cold temperatures through standard commercially available sensors. Among different technologies, superconducting microwave resonators have been recently investigated as ideal candidates for performing on-chip cryogenic thermometry, in reason of their intrinsically low power dissipation, large temperature sensitivities and excellent sub-μK resolution below 10 K. Through this study, we aim at demonstrating the possibility to enhance the temperature performance of superconducting microwave resonators by means of surface nanostructuring. Different arrays of nanotrenches are strategically patterned on the inductive line of a 1.3 GHz planar resonator, by partially etching a Nb₅₀Ti₅₀ thin-film, in order to tune the critical transition of the material and, therefore, increase the curvature of the fᵣₑₛ(T) response. Although the presence of such thinned superconducting regions introduces larger microwave losses, a 1.5 K decrease of TC is recorded, which directly translates into an enhancement of the temperature sensitivity by a factor 10, with respect to a non-nanostructured sensor. A maximum value of dfᵣₑₛ/dT = 62 MHz/K, at 4.2 K, is achieved for the device showing the largest nanotrench width of about 350 nm. These results demonstrate that such a surface nanostructuring approach can be exploited as an effective design strategy to tune the fᵣₑₛ(T) response of superconducting microwave resonators. Although this technique is found to introduce additional RF losses into the superconducting device, thereby limiting the achievable temperature resolution to the few-μK/Hz^(1/2) range, we believe that similar approaches could be further investigated for the development of future cryogenic sensors.