There's a question posted earlier today that described a situation where the OP is conflicted about getting their fan back from their colleagues, due to the extremely hot weather that they are all experiencing - here's the link:
My answer to their question, which agrees with an original answer and offers an alternative solution - purchasing a cooling vest - is a good one, imho, as I don't know how anything else but an alternative solution will do, in this unfortunate situation, especially since the OP has requested that no legal remedies be suggested and mentioned that no additional electronic devices would be allowed in the workplace.
Here was my answer, for those of you who don't have enough rep to see deleted content:
I agree with Daniel's answer that you would risk emphasizing your privilege over the people in the marketing department, so the answer to your question would be to simply not bring it up.
However, you had mentioned at the end of your question that you'd be willing to seek other solutions, so here's one:
Consider buying a cooling vest, which is not an electronic device; it's unpowered, so your boss could allow for this in the office - the vests are designed for people who work in very hot temperatures, e.g. people who work in a hot office, construction workers, dog walkers, people who work in oil fields, athletes, etc. It keeps you cool for about 2.5 hours, but if you have a freezer at your office, you can store additional cooling packs in the freezer and then use them later in the day. You can Google search or go on Amazon to look for a cooling vest, sometimes also known as an ice vest.
It's interesting to note that your willingness to seek an alternative solution, rather than demanding that the marketing department return your fan during this unfortunate heat wave, highlights several key interpersonal skills that you're using:
I then showed a couple photos of cooling vests.
Other answers are suggesting forceful action and legal remedies - which is what the OP doesn't want - and another answer suggests getting blindfolds for the office windows, which actually aligns with my goal of seeking an alternative solution, yet those answers are not deleted.
Can I get my answer undeleted?