Did Stannis see himself or another King in the night fire?

In A Storm of Swords Stannis says this to Davos:

“I know the cost! Last night, gazing into that hearth, I saw things in the flames as well. I saw a king, a crown of fire on his brows, burning... burning, Davos. His own crown consumed his flesh and turned him into ash. Do you think I need Melisandre to tell me what that means? Or you?”

^{-A Song of Ice and Fire: A Storm of Swords, Davos.}

He seems to imply that he thinks it is him who will burn because of his own crown. Stannis the Mannis has always taken his responsibility strongly [gritting intensifies], and clearly believes that he must see it through to the end, no matter what it costs himself. But we've already seen this exact scene happen with Viserys III.

So, does Stannis see himself in the flames or Viserys?