It's frosty? Where in Israel are you? I looked up climate for Jerusalem and there the coldest months are Dec and Jan, just like for me, but even so the lowest average minimum temps are above 0 deg C (i.e. freezing). That means it could be frosty in winter (I well know that temps below the average minimums are quite possible, since we just finished such a harsh winter). But it looks like frost in Jerusalem would be extremely unlikely in May and getting warmer from there.
"The climate of Israel is typically Mediterranean. It has long, hot and dry summers. This is followed by short, cool, warm and wet winters. Israel has heavy rainstorms that usually begin in November and end in March. Snow is possible in winter but only inland on high ground."
But yes, if you know what you are doing and IF YOU CAN PROVIDE ENOUGH LIGHT, peppers can be grown and set fruit indoors. That will have to be supplemental lighting, not just windows. My pepper plants that I start from seed under lights were already making blossoms before I brought them outside.
check out applestar's winter pepper threads:
https://www.helpfulgardener.com/forum/vi ... =4&t=55256
https://www.helpfulgardener.com/forum/vi ... 81&t=31055
there's another one called something like Winter Pepper Torture, which I was going to try to find for you. I found many threads referencing it, saying something like "you should look for the Winter Pepper Torture thread," but could not find the thing itself. If applestar sees this post, maybe she will be able to find it for you.
If you are not familiar with starting things from seed, please read the seed starting basics thread, here:
https://www.helpfulgardener.com/forum/vi ... 48&t=44183