Thanks @gardengal48 (PNW Z8/9) - my composting these days is simply ambient "worm buckets" which are at soil temperature (perforated 5 gallon buckets buried 95% in the planting bed. worms eat about 0.5 bucket per week). The hot setups sadly just did not work reliably in my situation.

Yeah, I forgot to add that achieving and maintaining those temps is not the easiest thing for a home composter to accomplish. It takes the right size pile, the right combo of ingredients and due diligence on the part of the composter :-)

I avoid composting thorny plants because I don't feel like taking the risk that they won't decompose as fast as everything else. If you have rhizome weeds or other things that regenerate from bits, I'd avoid putting those in the compost at all if you can't keep the pile hot (I can't either!) I've taken to keeping buckets of weeds in the garage because I don't want to risk baby weeds of whatever type. Either they wilt enough to take up less space in the trash, or they dry enough to use as tinder for family campfires. At some point I have plans to make a compost tea machine by putting a spigot in a 5 gallon bucket with a fine mesh bag with weeds in it, so I still get some value out of them.

I cold compost and I compost everything except fresh bindweed. I've never had a problem with weed seeds in the compost. Any seedlings which do appear are pulled and returned to the compost. In many decades of making compost I've never had a heap heat up nor worried about it.

What about nasty rhizome spreaders like the banes: fleabane, meadow bane, etc. They are horrible spreaders, and I'd hate to spread the roots in other beds via compost...

I don't compost the plants that spread by underground runners like those Christopher listed; throw mugwort onto that list too.

I try to keep out things that I know from previous experience stay fresh and green for months - pokeweed roots, dandelion roots, lady's thumb, purslane, some lawn grasses, bulbs; I usually put them in the garbage right away, but screw up sometimes and get them when I turn the heap over and pull out what's done. I cold compost, as I am too busy in the garden usually to turn the compost over with any regularity.

I compost all of the above, or at least those that I have here. Bindweed I only compost after it has been hung out to dry for a few weeks. I don't put anything green in the garbage. I cold compost the lot.

You are a brave, brave composter, floral.

What about cardamine aka hairy bittercress. Will the seeds survive composting? This is the most common annual weed in my garden and I would love to compost it.

Not brave, lisanti. Lazy. Or, as I prefer to think of it, pragmatic. I never do any garden chore unless I can see a benefit and since I've never had a problem with my methods I keep going.

I have composted Cardamine hirsuta In the past. But I rarely see it these days after years of cultivation on my allotment. I generally manage to get to any weeds before they set seed.

I'm so grateful for this help from @floral_uk z.8/9 SW UK, @lisanti07028, and @edenchild. I ponder these questions too.

I think I am persuading myself slowly to just compost more. After almost ten years with this garden I have come to accept that I have many billions of seeds and roots in the soil already, including a vast array of the "misplaced" invasive and non-natives from 50+ years of suburban gardening. Even if I am scrupulous in removing root fragments etc, these things will return, perhaps longer than me (maybe 10-15 years to go here in this property). Furthermore the squirrels, chipmunks, and hundreds of birds bring more random new plants almost all year long. Some of the obvious offenders here I am removing roots, seeds and fruits where it is easy/obvious etc (Hedera, Convolvulous, Taraxacum), and I am wary of random aggressive upstarts these days after the estimable @ken_adrian Adrian MI cold Z5 principle of principle of "if it pops up, it might be invasive".

In the end I have to balance my "cleaning up" tendency with my "let it live a little and identify", after all nature did bring me some lovely lupins that are now multiplying.