That looks really healthy to me. Picking all the fruit might induce it into producing flowers again. What really happens with some plants is that fruiting can inhibit flowering. This is not consistent for me among pepper varieties - some fruit and bloom continuously, others do better with an occasional pick-off-all-fruit event - and then they restart. With a short season, perhaps some plants would exhibit this phenomenon, but they don't get the chance. I've really seen this most dramatically on tomatoes (the determinate ones can be coaxed into a rebloom this way) - but some peppers seem to be like this too. You might also have a nitrogen excess - try cutting off or cutting down nitrogen fertilizer for awhile - and increasing P (mostly this) and K. Your pot is small (in ratio to the plant - but your plant looks just perfect) so the effects of this should be quick. Excess nitrogen is rarely a problem for me because of the low humidity, alkaline soils, and high level of sunlight - which stresses the plants so they can only take up so much nitrogen, but tomatoes can be sent on this path (though it's also a bit harder to do here than other places). I can't really see that you would have a heat problem in this location - on a balcony - unless you've had incredibly hot weather. Days over 95 F - for most of the day? I have a friend with a place down there and he say's it's not been that hot - though hot enough!
Lastly - stressing the plant a bit could help - though I would do this as a last resort. Let it dry out a little - till the leaves droop, then water. Just do this a few times, then back to normal. Sometimes this can induce flowering - but it's detrimental to flowering if it's already happening, so tread carefully. You have time there with great weather nearly all year - so no need to jump into drastic measures.