I am intending to apply for a PhD, but I lack prior research experience. I’m currently getting my master’s, but all of the labs at my university are full.
Therefore I am considering to join a lab at another university. The professor doesn’t know me; I will be cold-emailing them. How do I ask to join their lab? I don’t want to be paid, I simply want the experience. What do I do? Should I even reach out to this professor?
It's possible working without pay is not legal in your jurisdiction.
It's very likely the professor would like to (or is compelled to) focus on mentoring students at their same institution.
A cold email has a low success rate in the best of circumstances, these aren't the best circumstances, but that's all you really have. In your email be brief and to the point, use maybe a sentence to say what you want and a sentence to say why you're interested in that lab, attach your CV, and then plan not to hear a response (that's okay, you're taking a shot in the dark).
You certainly have an uphill battle. Each student a professor advises costs, on average, perhaps 2-3 hours per week if you include advising meetings, paperwork, reading thesis drafts, etc. Why would a professor offer this amount of time if it isn't part of their job duties at the university they're at? Why would a department agree to a professor using this much time if the university does not get the student's tuition or the state's subsidy for students?
In short, you're asking the person to do something out of the good of their heart, using time they could be spending with their family, gardening, reading books, riding bikes, or hanging out with friends. I think it's unlikely you're going to be successful -- regardless of how exactly you phrase your email.
You note that you are in the US. I suggest you apply to a variety of doctoral programs across the country. Cast a wide net, and you are likely to get into some doctoral programs. It may not be at your dream destination, but it is certainly better than being unpaid labor in a situation that is frankly not productive for you or your voluntary advisor.
While I work in a different field, I do get requests for remote supervision from students wanting to apply theory to our experimental work (usually foreign, or foreign students who got into a US program that is lower ranked/resourced than they had hoped). I always decline. This is not a reasonable arrangement, and frankly it violates many of the Conflict of Interest clauses at my University. I am using time and other resources to unofficially mentor a graduate student for whom the University can claim nothing (no degree conferred, no other metrics met).
