Could you clarify whether you are indeed mainly interested in suggestions how to earn money (as the last sentence of the post suggests), or rather in suggestions how to use your time during summer (as the title might suggest)?

I don't think this is an Academia question. Basically, it is a question of the sort "I am unemployed for a few months, how should I make some money?"

Have you looked into receiving your 9-month salary over 12 months? Might be useful if this is a situation you see repeating in the future…

I do think it is an Academia-relevant question, due to the common (in the U.S.) 9-month salaried period... with, apparently, the expectation that people win grants to pay summer salary, or teach during the summer, to generate income. As @Dawn comments, re-configuring your pay to have the 9-month pay paid out in 12 months is one way to self-budget, etc.

This is of course an Academia question. How could you have the question "What to do during Summer?" in industry?

@xngtng Yes, farmers are typical seasonal workers. So, the answers may be similar to the answers to this question. But, seasonal workers may not always have summer vacations. They may have some time in the year without income. I did not think of seasonal workers when I said industry. There is one thing you did not know, there are already 4 close votes for this question, one more will close this one. Hence my comment above.

@WolfgangBangerth, Rephrased. The question is, I have no grant. How should I get a paid position within academia?

I voted to reopen. I think the question would be better, though, without the last bullet point: the claim "Most professors, in USA, have very low 9 month salary (relative to their education and age)" is not backed up by statistical data in the question and will, anyway, be extremely subjective. What is or is not reasonable is also extremely subjective and I don't see how this is relevant to the question.

I'm with @JochenGlueck on that last point. The average 9-month salary of a full professor in mathematics at R1 universities is $120k or so -- about twice the median 12-month salary in the United States. Surely that does not qualify as a "very low" salary, and to claim that it is is whining at a rather high level.

@WolfgangBangerth The median professor isn't R1. The median annual wage of a postsecondary teacher is $79.6k.

@JochenGlueck, I agree that the "very" part may be subjective. The "low" part can be backed up by data, e.g., AMS 2019 salary survey: For public small universities, the Q1 and medium annual salary of associate professors in math (including applied) are $74,200 and $81,200, respectively. That's low for people with PhDs in their 40s that are competent enough to get tenure. The point here is that re-budgeting 9 month salary into 12 month is not very meaningful for an average professor. (Of course, I have a somewhat different definition of what average mean than @WolfgangBangerth)

Is the question - How can I get work as an adjunct at a different university? Or something else?

Perhaps you could tutor some subjects to one or more individuals that need some extra help? Not a boost for your career, but that would at least generate some income.

Teachers at all levels have the 'summer' off. Most of my US high school teachers had something else they did during the summer, and I'm sure they got paid much less than any tenure-track professor in the area. Convert to your 9-month salary paid over 12-months (a normal option).

I find the sentiment "I do not want to teach in Summer because there is no course in my area of specialty" to be extremely odd. I am a mathematician, a geometer/topologist. I routinely teach undergraduate classes in Calculus, Linear Algebra, Real Analysis, Complex Analysis..., whatever is needed. My attitude is that as a professional mathematician I should be able to teach any undergraduate class (some may require more preparation, some less).

@JonCuster - Yup. My father-in-law was a high school English teacher, and he sold shoes during the summer.

I feel this question, as a parent with 2 children and the standard 9-month (low) salary which is usually fine but a hurricane making me homeless and reduced summer classes (so taken by senior faculty) has ended that stretchability. However, I don't think it can realistically be answered or is really an academic issue. I've taken jobs ranging from retail to industry instructor based on availability, my skills, and luck - i.e. standard job search issues. And that's really it. Note, there are (some) answers to "short-term positions"

I find it sad that someone for whom money is important (or at least important enough that $70K is not a sufficient yearly salary) didn't know that academia is a bad idea if money is important.