Seems like stress from too much sun, too much water, and too much fertilizer. Peat pots cause problems with moisture control but probably help keep your full sun from cooking the rootballs as much as they wold with a plastic pot.
This is my method, which is fairly common.
Multiple seeds in small plastic cells full of damp potting mix (four or six packs from nursery seedlings). Sit cell pack in water to fully hydrate (~15 mins) set aside to sprout (4-5 days). When sprouting starts, sit under flourescent lights at room temperature, or in a large window away from the glass-heat.
When pots are light and mix seems dry (every 3-5 days depending on conditions) sit "pots" in water to rehydrate.
When the first true leaves expand and there is a bit of space between the leaves and the cotyledons I pull the roots apart to separate the plants and pot up in 3"-4" plastic pots or drink cups, burying the stem up to the cotyledons (this is probably at week 3). At this point, in the larger pots the plants need water less often until the plants grow larger and start to pull water from the soil. At the first watering after potting up (about 5 days later) I might use 1/4 strength fertilizer, but usually I wait a couple of weeks or don't fertilize at all until the last week or so before planting (week 5 or 6). At this time they may get extended periods of sunlight including midday sun), but before that only morning sun followed by bright shade (beginning shortly after potting up). Too much can go wrong with full sun on small seedlings, and I'm using April sun at higher latitudes with temps from 50-70. Your sun is brighter and temps are higher. If full sun can hit soil, not just leaves leaves, it can heat damp soil and cook the roots.