We demonstrate thermal imaging using a charge-coupled device (CCD) thermoreflectance lock-in technique that achieves a record temperature resolution of $18\mathrm{mK}$ , $44\mathrm{dB}$ below the nominal dynamic range of the camera (from 72 to $116\mathrm{dB}$ ) for ${10}^5$ periods of measurement. We show that the quantization limit of the CCD camera does not set the lower bound on the precision of the technique. We present a theoretical description of the measurement technique, accounting for the effects of noise and nonideal analog-to-digital conversion, resulting in analytic expressions for the probability distribution function of the measured signals, and allowing for explicit calculation of resolution and error bars. The theory is tested against parametrically varied measurements and can be applied to other sampled lock-in measurements. We also experimentally demonstrate sub-quantization-limit imaging on a well-characterized model system, joule heating in a silicon resistor. The accuracy of the resistor thermoreflectance measurement is confirmed by comparing the results with those of a standard $3\omega$ measurement.