I'm not sure what you're expecting of me here. As you say, our only source says the perpetrator was unknown. He literally says "by whom it was set on fire, nobody knows" (ὑφ᾽ ὅτου δ᾽ ἐνεπρήσθη οὐδεὶς οἶδεν). How are we to conjure up a case for the prosecution when, so far from us having any evidence at all, the only source even reporting this event specifically states that it was impossible to find a guilty party at the time?

And even if we could, why on Earth would we point the finger at Agesilaos? What possible purpose could be served by his burning down the temple of Poseidon? Are you suggesting this just because he ordered fire to be brought to his detachment on the heights overlooking the area in the line preceding Xenophon's remark about the burning temple? It should not need to be pointed out that these events are not related; the bringing of fire to the troops was about getting them warm, whereas burning the temple could have no such purpose. Are you suggesting Xenophon is covering up his friend's gross act of sacrilege in order to preserve his reputation for piety? But nothing obliged Xenophon to include the event in his narrative at all, so it would be absurd for him to mention it if there were actual rumours connecting it to Agesilaos. I just don't follow your line of thinking here. Why would Agesilaos do this?