Your transformers are 12VAC with a full load. The rectifier bridge rectifies the peak voltage of 17V at full load and maybe 19.6V without a load and the diodes drop the peak voltage to 18V.
You don't have a filter cap so the DMM reads the average of the fluctuating voltage, about 10V without a load.
The fridge probably has a filter cap that charges to the 18V peak voltage from the rectifiers.
Your circuit has three problems:
1) Cheap transformers have poor voltage regulation, even if you parallel a million of them. A single powerful transformer has pretty good voltage regulation because its windings have a much lower resistance.
2) A 12VAC transformer produces about 15VDC at full load when using a bridge rectifier and a filter cap. To get 12VDC the transformer must be only 9.9VAC at full load.
3) The bridge rectifiers have 1.25A of current and about 2V across them when powering the peltier. That's 2.5W of heat for each. A 10A bridge is rated with its case cooled to 25 degrees C, sometimes cooled to 70 degrees C. At its rated current, its internal temp is so high it is almost melting. How huge is your heatsink for them?