Temperature sensors are widely integrated in high performance systems, e.g. microprocessors. If the die temperature becomes too high, the processor must throttle its clock speed to prevent reliability problems. This application requires temperature sensors that can be integrated in the same advanced technologies as the microprocessor, and that can operate from the same low supply voltage. Since many temperature sensors are required, it is important that they only require a minimal amount of trimming. Thermal noise can be exploited as a temperature sensing principle in any technology with resistive elements. Since thermal noise is a fundamental physical phenomenon, it is inherently accurate and linear. The noise power only depends on the measurement bandwidth, which can be easily calibrated. Previous noise-based temperature sensors required very long measurement times to achieve decent resolution. This is because only small measurement bandwidths could be achieved with discrete measurement setups. By integrating the noise-thermometer on chip, and using the increasing speed of more advanced technologies to our advantage, resolution can greatly improve. This thesis presents the first on-chip noise-based temperature sensor. A prototype chip has been fabricated in a standard 160 nm CMOS process and it achieves a resolution of 0.93 °C in 1 s. The sensor can achieve an inaccuracy of 6.8 °C (3?) from -70 °C to 50 °C with a single point trim and an inaccuracy of 6.1 °C (3?) from -70 °C to 95 °C with a two-point trim. The sensor occupies a die area of 0.15 mm2 and consumes 1.9 mW from a 1.8 V supply. The design demonstrates that a pure electrical calibration should be possible, and both the resolution and accuracy are expected to improve in more advanced CMOS processes.