Trouble on the Balcony

After four and a bit weeks my first crop of radishes should be almost ready to eat, but all I've got so far are a bunch of leafy vegetables the shape and size of a snapped bookmaker's pencil. If you want your radishes to plump out, they need plenty of direct sunlight, a bit of heat and lots of moisture. The temperature on my balcony has, I think, been so hot that the shallow growbag soil is drying out too quickly (of course it hasn't helped that we haven't had any proper rain since the end of March). What I need is a deeper container and something to shade it from the sun, but for now all I can do is thin the plants out and hope for the best.