Is there a single noun in English for 'jerry-rigged?'

Besides Cool's good suggestion of
• slapdash (“Done hastily; haphazard; careless”, but I'd substitute not careful in place of careless)
and suggestion of
• slipshod (“Done poorly or too quickly; slapdash”, but I'd say slipshod work is lower in quality than slapdash work),

and the suggestions in comments of
• hack (“An expedient, temporary solution, meant to be replaced with a more elegant solution at a later date” or “A try, an attempt”),
• kludge (“an improvised device, usually crudely constructed” or “any construction or practice, typically inelegant, designed to solve a problem temporarily or expediently”),
• jury-rig (“To create a makeshift, ad hoc solution from resources at hand” with synonyms MacGyver and hack), and
• MacGyver (“To assemble, or cause to be repaired or completed, an object, device, machine, or project from duct tape as the preferred repair tool, but in its absence, other items, (normally common, ordinary and mundane such as a rubber band or paper clip)...”),

also consider
• lash-up (“A crude improvisation or bodged effort”),
• bodge (“To do a clumsy or inelegant job, usually as a temporary repair; patch up; repair, mend”), and
• stop-gap (“A temporary measure or short-term fix used until something better can be obtained”).

[Note, I edited my former answer into this sort-of-bulleted list, and added interpretive notes on slipshod and slapdash.]

My suggestion is "kludge." It was originally used for a computer program that was thrown together hastily and without regard for good practices, but it's slipped into the general vocabulary. For example, there's a book called Kludge, whose premise is that the human brain is one.

A nice single word for this is makeshift. This carries all of the right meanings, because it refers to something which is temporarily made to fit a purpose, and is of lesser quality than something more permanent and properly made. Something makeshift is almost the same thing as something jerry-rigged or jury-rigged.

Most other words do not cover the full range of meaning. For instance a hack or kludge is not necessarily something temporary. This word comments on the inelegance of a solution, which may actually be intended to be permanent. Sometimes only critics regard some work as a kludge or hack, not its creator.

The words slapdash and slipshod are also comments on quality, not on intent, as do words like botch, crap and so on. The latter is a somewhat crude word, because it is a synonym for feces and defecation, as a noun and as a verb, respectively. Slipshod work is intended to be permanent, but carried out in a way that lacks diligence. A slipshod solution is worse than a kludge, because not only is it inelegant or improper in some way, but it is also of poor quality and unreliable. Kludge solutions are sometimes perfectly reliable and long lasting. They just don't fit the surrounding design in some esthetic sense.

The word stopgap refers to something which temporarily fixes something which is broken. It literally refers to plugging a gap to stop a leak. For instance, it is possible to say that someone used a broomstick as a makeshift axle, but not as a stopgap axle. Some things which are stopgap cannot be makeshift. For instance, an emergency loan could be a stopgap solution to a cash flow problem, but it is not makeshift money.

A workaround is something which avoids a problem that cannot be fixed under the circumstances. Literally, it refers to a detour: working in such a way that the problem is somehow avoided, thereby making progress "around" it. If you use a heavy wrench as a substitute hammer, that cannot be called a workaround for the problem of not having a hammer, but you can call it a makeshift hammer.

The words impromptu and improvisation have a broader meaning, not specific to inventing a temporary solution. When a jazz musician improvises a passage, it is not some makeshift music to solve the problem that someone didn't compose the notes. Or at least, that would be a sarcastic view on the artform.

Bodge / bodged. Locally we would also say frigged, hacked.

Uses: "Bodge it up to make it work", "We don't have X but we could bodge something up to do the job", "That's a bodge-job" (bad job), "A bodged job"...

It can also just be "That's a bodge", "It's a bodge", etc. It's probably the most recognised term in UK English for what's being described, see Wikipedia's Bodger entry.

It's not always negative; respect is given for ingenuity, audacity, original thinking, and problem-solving, esp. in the face of urgent need, emergency, or adverse conditions.

From Oxford English Dictionary (OED) -

Cobble, n.