Can you post a picture? How much sun does it get per day? How big is the box?

Until knowing more, some ideas (I've had each of these in my window box over the years): geraniums, impatiens, periwinkles, salvia, verbena, rose moss, zinnias. My box is large, so I usually layer it--dracaena spikes or coleus in back for height, something flowering in middle, and potato vines or asparagus fern in front to trail.

These are wooden boxes about 3' long - I try to prolong their lives by planting in 6" pots - but even so, this might be their last year. House is oriented due north/south, so at the solstice, they would get several hours of full sun; there is no eave or overhang. Not so much spring and fall....

I have used impatiens before, but at the height of summer, it's too hot for 'em....

I'm in Texas, and my planter gets mostly sun ... amazingly, geraniums did really well. I expected them to burn up by August, but they stayed vibrant. The impatiens I had one year were a sun variety, and held up well, too.

Do you mean that your plants are in 6 inch pots and the pots are standing in the window box? If so the pots are really much too small for the plants to grow well. Can you get a cheap plastic box which would fit inside your wooden boxes? Or line it with plastic?