This paper demonstrates the use of voltage noise thermometry, with a cross-correlation technique, as a dissipation-free method of thermometry inside a CMOS integrated circuit (IC). We show that this technique exhibits broad agreement with the refrigerator temperature range from 300 mK to 8 K. Furthermore, it shows substantial agreement with both an independent in-IC thermometry technique and a simple thermal model as a function of power dissipation inside the IC. As the device under a test is a resistor, it is feasible to extend this technique by placing many resistors in an IC to monitor the local temperatures, without increasing IC design complexity. This could lead to better understanding of the thermal profile of ICs at cryogenic temperatures. This has its greatest potential application in quantum computing, where the temperature at the cold classical-quantum boundary must be carefully controlled to maintain qubit performance.