Heat, and lots of it
Peppers germinate poorly below 20 °C (68 °F) and well at 25–30 °C (77–86 °F). If your room is cool, germinate the seed on damp paper in a sealed bag somewhere warm — on top of a router, above a fridge — and move it to the system only once it has sprouted.
Once growing, they want warmth more than almost anything else. Reservoir at 20–24 °C (68–75 °F) is right. Below 15 °C (59 °F) growth stops; below 10 °C (50 °F) the plant is damaged. This is the one crop where the chiller's job, like basil, is keeping water warm rather than cool.
They also want strong light. A windowsill gives a leggy plant with a few small fruit; proper supplemental light gives a compact bush loaded with them.
Feeding a fruiting plant
Start at EC 1.2–1.4 while the plant is small, then raise to 1.8–2.2 once it is flowering and setting fruit. pH 6.0–6.5.
Peppers are prone to blossom drop if they are fed too heavily during flowering, and to leaf-edge burn if the EC spikes. Steady is more important than strong — keep the reservoir consistent rather than chasing a high number.
Calcium matters for fruit quality. Inconsistent watering is the usual cause of a sunken brown patch at the tip of the fruit, the same distribution problem as tomato blossom end rot. Keep the level stable and the water cool, and do not add calcium expecting a fix.
Pruning and support
Pinch out the first flower that appears on a young plant. It costs you a week and produces a bushier plant that fruits far more heavily over the season.
Most annuum varieties grow 40–80 cm (16–31 in) and will need a single stake — a fruiting plant becomes top-heavy and will lean out of the net pot. Tie loosely with soft twine.
Remove lower leaves that touch the lid. They stay wet, they shade nothing useful, and they are the first thing to go mouldy in a still room.
Harvesting, and the heat question
Pick green for a milder flavour and a plant that keeps producing. Leave fruit to ripen to red, orange or yellow for more sugar and more heat — but be aware the plant slows production while fruit is ripening, so a plant left to fully ripen gives fewer, better fruit.
Heat level is genetic, not nutritional. Nothing you add to the reservoir makes a pepper hotter. Stress — particularly water stress — can concentrate what is there, but it cannot create capsaicin that the variety does not produce.
Saving seed, and a warning
Peppers are self-pollinating but insects cross them readily, and all annuum varieties cross with each other. Isolation of 30–60 metres (98–197 ft) is the usual figure; in a garden, grow one variety for seed or bag the flowers.
The heat problem. If a hot variety crosses with a sweet one, the seed carries the cross but the fruit of the current generation does not show it — the heat appears in the next generation. That means you can save seed from a sweet pepper that was pollinated by a chilli, plant it, and get a plant that produces hot fruit. There is no way to tell from the seed.
This is why seed savers keep one annuum per year, or bag. It is also why "sweet pepper" seed from an open garden is a gamble.