Some applications require electronic systems to operate at extremely high temperature. Extending the operating temperature range of automotive-grade CMOS processes -- through the use of dedicated design techniques -- can provide an important cost-effective advantage. We present a second-order discrete-time delta-sigma analog-to-digital converter operating at a temperature of up to 250 $^\circ$C, well beyond the 175 $^\circ$C qualification temperature of the automotive-grade CMOS process used for its fabrication (XFAB XT018). The analog-to-digital converter incorporates design techniques that are effective in mitigating the adverse effects of the high temperature, such as increased leakage currents and electromigration. We use configurations of dummy transistors for leakage compensation, clock-boosting methods to limit pass-gate cross-talk, and we optimized the circuit architecture to ensure stability and accuracy at high temperature. Comprehensive measurements demonstrate that the analog-to-digital converter achieves a signal-to-noise ratio exceeding 93 dB at 250 $^\circ$C, with an effective number of bits of 12, and a power consumption of only 44~mW. The die area of the converter is only 0.065~mm$^2$ and the area overhead of the high-temperature mitigation circuits is only 13.7%. The Schreier Figure of Merit is 140~dB at the maximum temperature of 250 $^\circ$C, proving the potential of the circuit for reliable operation in challenging applications such as gas and oil extraction and aeronautics.