You got it, same seed in practice, but also just temperature = 0 for the demo actually. A few things I considered adding for the fun of it were 1) a way to specify a seed in the input text, 2) a way to using a symbol to say "I didn't like that token, try to generate another one", so you could do, say, "!" to generate tokens, "?" to replace the last generated token. So you would end up typing things like
"Once upon a time!!!!!!!!!!!!!!!!!!!!!!!!!!!!!SEED42!!!!!??!!!??!"
and 3) actually just allow you to override the suggestions by typing what letters on your own, to be used in future inferences. At that point it'd be a fairly generic auto-complete kind of thing.