[Phantom]

I know that they work better with a larger temperature differential but how large do you need?

At some point it will not generate more energy even if you add more heat.

Looking at the spec sheet you linked to the best conversion rate is cold 30C (86f) and hot between 150-225C (302-437F). So you only need about 216f to 351f difference.
When the hot side is increased to 300C or a temp difference of 486F the conversion rate drops from 6% to 5%.

I would assume that the above numbers happen due to how fast the material can shed the heat on the cold side before it gets heat soaked and the temp differential goes down.