80 is very hot for parsley. But what I am mainly thinking on reading your post is why are you starting parsley indoors in Zone 9 at all? Parsley grows a tap root and although it can be transplanted it is prone to bolting. If you direct sow you have not transplanting worries and no overheating worries. Parsley comes from temperate climates. Tomatoes and Peppers from tropical climates. Knowing their antecedents is a guide to knowing how to care for them.

Here's the problem: My Zone 9 temps, at the moment, can range from 55-47, with the occasional 60 degree day. That's a little chilly, even for parsley. Plus, I live in an apartment with very little sun on my deck-- it may like partial sun, but I think it needs more than three hours' worth. And to tell you the truth, I'm not too worried about bolting. The way we eat parsley around here, I'm just hoping it gets a chance to root before it's devoured. :)

Right, I see. You didn't tell us you had no outside garden space originally.The problem is that you have the parsley in with the heat lovers. 80 is OK for germination but the plants need much lower temperatures after that. Your current temps are fine for parsley plants (once hardened off). Mine has been outside all winter and my temps are very similar at the moment. Is there any way you can prick out the parsley into different containers and start hardening them off? Your sun situation, while maybe not ideal, will not faze parsley imo. If you are happy to allow bolting you'll need to keep sowing in succession to provide new plants or you won't have any parsley later in the year.