The open fermenter may ferment cooler due to the insulation of a lid, just as a pan with a lid on boils faster, but I can see the difference being huge. that is all things being equal.
One difference that could potentially affect things regarding temperature would be the availability of dissolved oxygen, with more O2 available the yeast should be able to replicate faster and metabolise faster generating more heat.
The partial pressure of CO2 will be lower in an open fermenter and that of O2 higher vs a closed fermenter but not sure this will affect the temp. This can aid yeast in the first few days to establish a healthy fermentation as O2 is required to build properly functioning cell walls.
Another thing to mention is many traditional open fermenters are shallow and have a large surface area that would allow more efficient natural cooling than the modern cylindroconical stainless fermenters.