There are two answers: hold the chemistry at 38°C, or add time to make up for the drift.

C-41's standard temperature is 38°C and the developer step is around 3 minutes 15 seconds. Because the step is short, a one-degree error matters — this is where home colour development usually goes wrong.

Option 1: hold the temperature. Sit the bottles in a tub of 40–43°C water, wait until they read 38°C, and start. In winter the bath cools during the run, so you top it up. Plenty of people repurpose a sous-vide cooker or an aquarium thermostat; anything that controls to 0.5°C works.

Option 2: compensate with time. Warm the chemistry roughly, and when the temperature drifts during processing, extend the development time to match. The AGO Film Processor works this way, which removes the need for a temperature-holding device at all. Note that time compensation only runs in rotary (horizontal) mode — stood upright for stick agitation, the temperature probe is not in the liquid, so compensation switches off.

A lower-temperature process around 30°C also exists, but fewer kits support it.

For what it's worth, C-41 is only three steps — colour developer, blix, stabiliser — so once temperature is solved it is simpler than black-and-white.