Superconducting microwave resonators have recently gained a primary importance in the development of cryogenic applications, such as circuit quantum electrodynamics, electron spin resonance spectroscopy and particles detection for high-energy physics and astrophysics. In this work, we investigate the influence of the film thickness on the temperature response of microfabricated Nb50Ti50 superconducting resonators. S-shaped split ring resonators (S-SRRs), approximately 20nm to 150nm thick, are designed to be electromagnetically coupled with standard Cu coplanar waveguides (CPWs) and their microwave properties are characterised at temperatures below 10K. The combined contributions of the kinetic inductance LK(T) increase and the decreasing loaded quality factor QL, for thinner films, induce an optimum condition on the temperature sensitivity and resolution of the resonators. A noise equivalent temperature as low as (0.53 +/- 0.09)mu KHz-1/2, at 1Hz, is reported for 100nm thick resonators at 4.2K. We also asses the possibility of implementing a multiplexed frequency readout, allowing for the simultaneous temperature tracking of several sensors along a single CPW. Such results demonstrate the possibility to perform a distributed cryogenic temperature monitoring, with a sub- mu K resolution. Thus, the application of superconducting S-SRRs, eventually benefiting from an even higher LK(T), for a further miniaturisation, as well as a back-end integration directly on-chip, can be envisioned for the accurate monitoring of localised temperature of devices operating in cryogenic conditions.