The development of quantum electronic devices operating below a few Kelvin degrees is raising the demand for cryogenic complementary metal-oxide-semiconductor electronics (CMOS) to be used as in situ classical control/readout circuitry. Having a minimal spatial separation between quantum and classical hardware is necessary to limit the electrical wiring to room temperature and the associated heat load and parasitic capacitances. Here, we report prototypical demonstrations of hybrid circuits combining silicon quantum dot devices and a classical transimpedance amplifier, which is characterized and then used to measure the current through the quantum dots. The two devices are positioned next to each other at 4.2 K to assess the use of the cryogenic transimpedance amplifier with respect to a room-temperature transimpedance amplifier. A quantum device built on the same substrate as the transimpedance amplifier is characterized down to 10 mK. The transimpedance amplifier is based on commercial 28 nm fully depleted Silicon-on-insulator (FDSOI) CMOS. It consists of a two-stage Miller-compensated operational amplifier with a 10 MΩ polysilicon feedback resistor, yielding a gain of  V/A. We show that the transimpedance amplifier operates at 10 mK with only 1 μW of power consumption, low enough to prevent heating. It exhibits linear response up to ±40 nA and a measurement bandwidth of 2.6 kHz, which could be extended to about 200 kHz by design optimization. The realization of custom-made electronics in FDSOI technology for cryogenic operation at any temperature will improve measurement speed and quality inside cryostats with higher bandwidth, lower noise, and higher signal-to-noise ratio.