Same here: FP3+ died last week with no warning, a little less than 3 years old. No immediate drop or accident involved, it was just in my pocket when it happend, with the battery at 70%. However I must admit that the phone had to endure quite a large amount of drops in the months before (favorite amusement for our child at the moment is to grab phones and throw them around).
Unfortunately, my backup HDD was faulty and the last working copy was more than 1 year old. (Remember not only to backup, but also to check the integrity of your backup!)
I was able to boot into OS (LineageOS) a day later once, but it only took 1 minute to die again. From then on, either no reaction or just a few seconds of the Fairphone logo and then black again. From what I read here, I was quite sure that the motherboard was the problem. So I tried the baking solution.
The side with the majority of the spring contacts facing upwards, supporting the two spring contacts on the other (bottom) side with a few layers of baking paper. Remember to remove all connector cables and the protective plastic film below them.
First I tried 10 minutes at 180°C, but that did not work. Then I gave it another 10 minutes at 200°C, and that did the trick. (You have to let it cool down in the oven without moving it.) It smelled a little weird when I opened the oven door, so you should ventilate your kitchen after the treatment, and propably also clean your oven after the procedure.
It’s working for more than 24h now, but I don’t really trust it. 
But even if it’d die again tomorrow, it gave me enough time to recover my data.
Thanks to @HolosericaCaligo and all others for sharing your experiences!