I don't know what the temp in your basement is in general, but the air temp around the foliage (plant canopy) is what matters to the plants, and what they respond to. If the temp is lower/higher on the wall thermostat, that's not an accurate reading. The temp at the foliage is what maters to the plants. If I remember correctly you even said at one point, the plants foliage was burning when it got close to the
lights.
I would take a regular thermometer and place it near the top of the plant canopy (closest to the heat source). I'm not familiar with all types of lettuce, but don"t think your lighting cycle has any thing to do with it. You are at almost a 50/50 cycle with 13 on, and 11 off. They should be fine with more than that on. But the light source is most likely the cause of heat source to the plants. But I would also check the temp of the
nutrient solution. If it's high, it could also be adding to the heat problem for the plants. It should be in the low 70's as well. I just use a inexpensive $2 fish tank thermometer to check mine. Also, can you elaborate on the lighting?
P.S. You said it was a aquaponics system, can you elaborate on that because I cant tell much from the pictures. If it's a real aquaponics system you may have a nutrient problem as well. Also if you are just using fish emulation or bat guano etc. and just considering it a real aquaponics system, well that's even worse. I just cant tell anything in that regard from the pictures. Along with any possible heat issues, true aquaponics is more complicated than hydroponics. But using fish emulation or bat guano instead of live fish is not compatible, but possible with enough trial and error. As well as the addition of microbes.