Erythromelalgia (EM) is a rare disease, which is still poorly characterized. In the present paper, we compared the hand perfusion of one female EM patient, under challenges, with a healthy control group. Using a laser Doppler flowmeter (LDF) with an integrated thermal probe, measurements were taken in both hands at rest (Phase I) and after two separate challenges—post-occlusive hyperemia (PORH) in one arm (A) and reduction of skin temperature (cooling) with ice in one hand (B) (Phase II). The final measurement periods corresponded to recovery (Phases III and IV). The control group involved ten healthy women (27.3 ± 7.9 years old). A second set of measurements was taken in the EM patient one month after beginning a new therapeutic approach with beta-blockers (6.25 mg carvedilol twice daily). Z-scores of the patient’s LDF and temperature fluctuations compared to the control group were assessed using the Wavelet transform (WT) analysis. Here, fluctuations with |Z| > 1.96 were considered significantly different from healthy values, whereas positive or negative Z values indicated higher or lower deviations from the control mean values. Cooling elicited more measurable changes in LDF and temperature fluctuations, especially in higher frequency components (cardiac, respiratory, and myogenic), whereas PORH notably evoked changes in lower frequency components (myogenic, autonomic, and endothelial). No significant Z-score deviations were observed in the second measurement, which might signify a stabilization of the patient’s distal perfusion following the new therapeutic approach. This analysis involving one EM patient, while clearly exploratory, has shown significant deviations in WT-derived physiological components’ values in comparison with the healthy group, confirming the interest in using cold temperature as a challenger. The apparent agreement achieved with the clinical evaluation opens the possibility of expanding this approach to other patients and pathologies in vascular medicine.