This article presents a body-heat-powered, multi-sensor SoC for measurement of chemical and biological sensors. Our approach combines analog front-end sensor interfaces for voltage- (V-to-I) and current-mode (potentiostat) sensors with a relaxation oscillator (RxO) readout scheme targeting $\ll$10 $\mu$W power consumption. The design was implemented as a complete sensor readout system-on-chip, including a low-voltage energy harvester compatible with thermoelectric generation and a near-field wireless transmitter. A prototype IC was fabricated in a 0.18 $\mu$m CMOS process as a proof-of-concept. As measured, full-range pH measurement consumes 2.2 $\mu$W at maximum, where the RxO consumes 0.7 $\mu$W and measured linearity of the readout circuit demonstrates R$^{2}$$>$0.999. Glucose measurement is also demonstrated using an on-chip potentiostat circuit as the input of the RxO, with a readout power consumption as low as 1.4 $\mu$ W. As a final proof-of-principle, both pH and glucose measurement are demonstrated while powering from body heat using a centimeter-scale thermoelectric generator on the skin surface, and pH measurement is further demonstrated with an on-chip transmitter for wireless data transmission. Long-term, the presented approach may enable a variety of biological, electrochemical, and physical sensor readout schemes with microwatt operation for batteryless and power autonomous sensor systems.