For this you will NOT need any kind of Controller. As you describe the system, you say each fan is fed a constant 12 VDC at all times from some power supply, and there is NO means of altering the fan speeds. I presume that means each fan has TWO wires to it. On a normal computer fan, these would feed into Pins 1 (Ground or -) and 2 (+12 VDC supply). No other connections. That does not require any Controller system.
That system you have uses a Peltier type of cooling device, which can move heat at only modest rates, so the fans involved do not need to be super-high-power ones. But since they are mounted on finned heat exchangers as I expected, they should be ones designed for "pressure" applications, not "air flow". If you have specs to read, that means their pressure rating in mm of water should be well over 1, preferably close to 2 or even higher. I suggest you look through the models made by Noctua
Noctua's premium fans are internationally renowned for their superb quietness, exceptional performance and thoroughgoing quality.
noctua.at
That's their master list, on several tabs. Do not consider their Industrial PPC line - they are very high-power units that consume more electric power, can blow at high rates you do not need, and create more noise. I suggest the Redux line. That is their older design but still very good, and slightly cheaper than newer products. (Some users are not happy with the colours of those fans, but that probably does not matter.) Click on the Redux tab, scroll down to the size group you have found, and look at details of 3-pin models. Click on one fan name in the left column to get detailed specs. A small note if you are comparing with other maker's spec sheets. Noctua specifies the fans' max air flow in m³/hr, whereas Americans always use CFM. To convert, CFM = m³/hr x 0.589.
In general comparison to other makers, Noctua fans deliver pretty high air flow for the same electrical current consumption, relatively low noise, and have long lifetime - warranty typically is 6 years, and most users say these fans do exceed that lifetime.