"Sterilizing" the manure isn't going to equal compost, AFAIK. IMO the high temps will destroy much of the "good stuff".

I'm not sure how effective your strategy will be with the facts given...attaining seed killing temps in "muffins" that are insulative may be problematic.

I often just let the seeds sprout and either throw back in the compost or on the mulch.

>> IMO the high temps will destroy much of the "good stuff".

I don't see why replicating the same high temperatures that a normal hot compost pile achieves would destroy the good stuff. Consider the info at the link below. Particularly the second section, Advantages of Hot Composting. It looks like I should be able to achieve pretty good weed seed destruction at 150 degrees for 2 hours.

Here is a link that might be useful: Hot Composting

Cut the compost in to the bed & wait. When the seeds sprout, cover with clear Plastic for a day or so, killing the weeds.
You could just mulch heavy, many no till gardener never turn the compost. They lay it on top, so seeds can get in the beds from compost, birds, wind. They just mulch. The Great Ruth Stout did not pull weeds, she lay them down & covered them with rotten straw, they rotted too.

Mulching over weed seeds works fine for large plants like tomatoes or peppers but not so good for intensively planted carrots. I have a specialized raised bed (4x16 feet) for carrots which I amended with a lot of sand and organic materials and then I solarized the whole thing last July before planting my fall carrots. It worked great and I had hardly any weeds. I planted about 10 rows of carrots (Napoli) in this bed and harvested them throughout the winter. (I mulched the bed heavily to prevent the carrots from freezing. Anyway, my point is that I don't want to add weed seeds to this bed now that it is nearly weed free, but I would like to add some more organic material (not manure) before planting my spring carrots. I have another source of milder organic material (city leaf pile) but it has lots of seeds too so I'd like to try to sterilize that as well.

Composting is always better for most any waste material from the garden and any animal manure we can get. The bacteria that convert that material from waste into compost conserve the nutrients that are there and make them into nutrients plants can use. "Weed" seeds not only travel in animal manures but on the wind and with birds flying over.
It may be that I am more Lazzes Faire but I don't obsesse over potential "weeds" growing in the garden especially since mulches will usually control them.

Steve, when I first started composting I believed "hot" composting was the only "true" compost. I strove to get the highest temps possible. I noticed many of the things your link points out in the "cons" section...LOTS of time and labour involvement, fussiness with C:N in the pile composition, and constant moisture make-up.
Also, N loss through outgassing. My reading suggested this was not optimal, and there are too many other things to do with the time.

Insult to injury, it didn't kill "weed" seeds.(Actually, the manure I get largely contains cereal grains). To break apart the manure to expose everything to high protracted temps would involve either labour or mechanical input (shredder of some sort) and I'm against energy use for small or no gain.

I'd suggest sifting finished compost for addition to your carrot bed...as mentioned earlier, let any seeds sprout and add back in during the making.

And as Kimmsr points out, nature abhors a vacuum. You're going to have weeds no matter what.