Where do you live, BTW. I could never get a pepper seedling, sprouted in October, past my climate's horrid, no-sun winter. Some sprouts from March have made it, but never even a February seed has done more than suffer in my area. I have tried (I'm serious - for years - with all manner of sun gathering equipment, soil warming devices and other blah, blah - it doesn't work) and it is mostly the May seedlings which come to mature fruiting.
If you live in Arizona - maybe. I would dearly love to try!!
I'm in Florida. Hot like Arizona, but unlike Arizona it's very humid here instead of dry. It's starting to cool down here, relatively speaking. Around here, 60 degrees Farenheit is considered chilly. That might sound wonderful, but hurricane season's a bitch. I suppose I could bring the sprouts inside if it gets too cold, and put them back out in the spring.
I looked at them again this afternoon, and there's definitely sprouting going on.
If this experiment fails, I'll just try again in the spring. (Remember, it was free. I was cutting up a grocery store pepper for lunch and had some potting soil left over from the maple, so I figured "what the hell".)
Well, then, COOL!
I grew up in the southernmost tip of Texas, so I know a little about warm winters (and I've studied hurricanes and horticulture). I was eighteen when I first encountered snow. Still hate it! (I now live in Indiana ...

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You might be OK (- for some reason, I thought your were Eurotrash or something. SORRY! It's the screen name, but we'll talk about that later.)
Beware the sneakiness of fungi! Don't allow seedlings to stay wet, and keep the air moving.
What I would do (if I had fresh seeds and a southern winter to look forwad to) is I would make sure to use only fresh, sanitized sphagnum moss and plant some seeds about every two weeks. That way, if you get an infection, you can control it with acidic sprays (citric or acetic acid sprays - low concentration) and likely many from less susceptible ages would survive. Then as the weather becomes more to the liking of the tropical pepper plants, some will have well established roots. Combine these efforts with warming the actual soil where they are to be planted and again setting them out in succession - what ever type of seeds you have - some should make it to maturity. No guarantee that they will produce fruit, but you will know with the first flower whether or not they are capable.