Are chillies hotter when they're ripe?
McGee writes: "Capsaicin appears to accumulate in the fruit concurrently with the pigment during ripening". (On Food and Cooking, p.212)

So yes, chilis get hotter as they ripen (that is, as they turn from green to red). Many chili varieties are picked and sold in stores while still unripe and green (e.g. jalapeño, serrano, poblano), but you will occasionally see ripe, red ones in stores. 

All of the dried chilis I've seen in stores have been completely ripened before drying (e.g. chipotles, which are smoked, dried red jalapeños and anchos, which are dried, red poblano peppers).

I've personally observed this effect with padron peppers, which are usually picked green and mild, but can ripen to red, hot peppers if left on the plant.