Can you please explain the difference?
1. I hope the WiFi works when I'm writing my bachelor‘s thesis.
2. I hope the WiFi is working when I'm writing my bachelor‘s thesis.
3. I hope the WiFi works when write my bachelor‘s thesis.
Sentence (3) is ungrammatical, but I believe you made a typo. I think you meant to type "I" between "when" and "write":
(3') I hope the WiFi works when I write my bachelor's thesis.
Now the sentence is grammatical, but it is the oddest sentence of the three. It could be interpreted as suggesting that writing your bachelor's thesis will cause the WiFi to work.
A: The WiFi isn't working.
B: Have you tried writing your bachelor's thesis?
A: No. Good idea. I hope it works when I do.
I'm being facetious, of course. The above conversation is silly. Sentences (1) and (2) are better than (3). I don't think it's necessary to double up on the progressive, though. Putting it in one of the clauses is enough. I like (1) better than (2), but both are fine. Here's another permutation that works. Perhaps you meant to include it:
(4) I hope the WiFi is working when I write my bachelor's thesis.