Raynaud's Phenomenon (RP) is a paroxysmal vasospastic disorder of small arteries, pre-capillary arteries, and cutaneous arteriovenous shunts of the extremities, typically induced by cold exposure and emotional stress. RP is either primary (PRP) or secondary to systemic sclerosis. In this study we use Control System Theory to model finger thermoregulatory processes in response to a standardized cold challenge (a diagnostic test routinely performed for differential diagnosis of RP). The proposed model is based on a homeostatic negative feedback loop, characterized by five distinct parameters which describe how the control mechanisms are activated and maintained. Thermal infrared imaging data from 14 systemic sclerosis subjects (SSc), 14 PRP, and 16 healthy control subjects (HCS) were processed. HCS presented the fastest active recovery, with the highest gain. PRP presented the slowest and weakest recovery, mostly due to passive heat exchange with the environment. SSc presented an intermediate behavior, with the longest delay of response onset. The estimated model parameters elucidated the level of functional impairment expressed in the various forms of this disease.