The thermoacidophilic red alga Cyanidioschyzon merolae survives its challenging environment likely in part by operating a carbon-concentrating mechanism (CCM). Here, we demonstrated that cellular affinity of C. merolae for CO2 is stronger than the rubisco affinity of C. merolae for CO2. This provided further evidence that C. merolae operates a CCM while lacking 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 previously described in detail. The results supported the feasibility of this proposed minimal and non-canonical CCM in C. merolae. To facilitate robust modeling of this process, we incorporated new physiological and enzymatic data into the model, and we additionally 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 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 novel CCM could exist in C. merolae and illuminated essential features necessary for CCMs to function.