Approaching a company unsolicited for internship opportunities as an academic It's already been discussed on here how to find internships/temporary research opportunities at universities and also when exactly to do an an internship at a company during one's PhD, but there doesn't seem to be much information on how someone goes about finding internship/temporary research opportunities at companies.

There are a few companies which do stuff which is very similar to what I'm researching, and a couple of those are even posting full-time jobs for work nearly identical to my own albeit looking for people who are more experienced in the field than I currently am. How can I approach said companies which are actively working on my own research topic (more or less) with a proposal to spend a period of time working with them?
I think it makes a difference whether you want to ask about a paid versus unpaid internship - companies may be more likely to agree to an unpaid internship. However, you could reach out to someone who would be in an authority position related to the job announcement you already found and ask if there are any opportunities to gain experience through an internship. The worst they can say is no.