Might be fixable with promoting and/or a much lower temperature?
Ask some model to generate a number uniformly between 0 and 100; you get 47 a lot. Or 27. Something like that.
Ask it for a list of numbers, uniformly distributed, and it also often starts with the same number. However later elements in the sequence will converge (imperfectly) to a better approximation of uniformity.
The same for names of the dwarves and paladins in your party.