It's a nice exercise to try to calculate total inductor loss (core/hysteresis loss and copper loss) and to use core volume to estimate temperature rise...
Depending on how accurate your calculations are, it might just be betterto just print it out of the best material you have access to and check the temperature rise with thermocouple, IR, etc.
distributed air gap on each leg
Also, I think you had another thread talking about gapping all three legs, right? Just another reminder that this does not make it a distributed air-gap (it's not powder/alloy core), and please be mindful of gapping the outer legs for fringing fields/EMI control.