The thermoacidophilic red alga Cyanidioschyzon merolae survives its challenging environment likely in part by operating a carbon-concentrating mechanism (CCM). Here, we demonstrated that C. merolae's cellular affinity for CO2 is stronger than the affinity of its rubisco for CO2. This finding provided additional evidence that C. merolae operates a CCM while lacking the structures and functions characteristic of CCMs in other organisms. To test how such a CCM could function, we created a mathematical compartmental model of a simple CCM, distinct from those we have seen previously described in detail. The results of our modeling supported the feasibility of this proposed minimal and non-canonical CCM in C. merolae. To facilitate the robust modeling of this process, we measured and incorporated physiological and enzymatic parameters into the model. Additionally, we trained a surrogate machine-learning model to emulate the mechanistic model and characterized the effects of model parameters on key outputs. This parameter exploration enabled us to identify model features that influenced whether the model met the experimentally derived criteria for functional carbon concentration and efficient energy usage. Such parameters included cytosolic pH, bicarbonate pumping cost and kinetics, cell radius, carboxylation velocity, number of thylakoid membranes, and CO2 membrane permeability. Our exploration thus suggested that a non-canonical CCM could exist in C. merolae and illuminated the essential features generally necessary for CCMs to function.