No, we wouldn’t recommend using a curler or flat iron/straighteners on your hair while scalp cooling. Any heated styling products may cause additional damage to you hair that will already be drier as a result of chemotherapy. Using these tools can also put additional tension at the roots of the hair, which should be avoid while scalp cooling.
We would only recommend using a blow dryer/hair dryer on a cool, low setting, and use your fingers rather than a blow dry brush to avoid additional tension at the roots of the hair.