Can I renegotiate my salary when moving from temporary to permanent employment?

If you are offered a permanent job, you should get a new contract, as a permanent job is a different form of employment. When you sign a new contract, you can certainly negotiate your employment conditions. Above all, it is important to look at what your duties and responsibilities will be - will you have any new tasks or new responsibilities? Often, it can be the case that more responsibility and tasks are assigned to permanent employees rather than people with fixed-term contracts, and this should of course be compensated in the pay envelope.
As a member of Naturvetarna, you have the opportunity to receive salary coaching in our member advisory service. We can help you with statistics and arguments for the salary negotiation. You can find our contact details and opening hours here: Member advice - Naturvetarna