I'm an external PhD candidate at a university in Germany, meaning that I have neither a post at the university nor funding. I know this isn't ideal, but my question is this:
My research is related to language education, and for my field work I'd like to compare students from a certain Asian country (mine) with German students. I have done the field work in Asia, and now I need to teach a class in at least two German universities to observe the students' attitude first-hand.
Would it be very outlandish to write an email to a department chair at a neighbouring university in order to propose a class in relation to my PhD project? I've checked their program, and the title of my proposed course isn't there. As this is for the sake of my project, I could do it voluntarily, although I'd be very glad if I'm paid. Should I state that as well (at least the first part)?
I have no idea whether an unsolicited application like this is common in academia (particularly in Germany). In any case I don't want to sound desperate or forcing someone's hand. Thank you in advance for your insight.
P.S. My supervisor is taking a sabbatical leave, so he's not around at the university, and I cannot easily ask questions like this.