1) Definitely not when it's hot.

2) I don't have enough experience yet, but I would guess that Spring is the best time to do so. Plants are going into general growth mode (most of them, anyway) and the transplants will have many months to grow into their new homes.

The other time would be fall, but in my little gardener's medula oblongata that time would not be the most advantageous.

As for unsolicited information, there's not much you need to know about Agaves that don't also apply to other plants, but be prepared to chop - their roots are very fibrous. Also, wear some chest/arm protective gear - not only for the incredible spines, but the sap from the leaves can be quite the unpleasant experience for some.

Transplants should be done at the beginning of the growing season(s). It is important that plants not be exposed to stressful conditions (very cold, hot, or wet) within a couple of months after transplantation. In pots in a controlled environment, you can transplant anytime, but outside, the best time depends on your local conditions.

Transplantation should be done early enough for the plant to get over shock and to develop new roots before stressful environmental conditions occur. In areas with hot summers and cold winters, transplant in early fall or early spring. I think it's probably too late to do this year. Wait until overnight lows are above 40F before transplanting in early spring.

Brad

And to add to Brad's advice,

I personally would put some bone meal in with the soil, along with any other amendments you would normally use (if any), and wait several days before watering it in (whether you do with transplant juice or not is up to you - I would); this will give a chance for the roots to seal off and start healing.

I was going to suggest leaving uprooted plant's roots out in the air for at least a week so that any injuries callous over, preventing fungal infection. Then plant, and wait a couple of weeks before watering. There is no rush. I have left relatively small plants sitting out for over a year without soil. They dry up quite a bit, but they don't die for a long long time. Waiting a few weeks won't hurt your plants, and may prevent rot.

Jeff's advice about wearing armor is a good one. Fireplace gloves (the big heavy kind) make very good hand protection. Also, make sure to wear eye protection! It is very easy to poke out an eye while working around large agaves. It may be helpful to trim the ends off lower leaves to give you more access.

Take some pics of the project. I'd love to see your plants. ;)

I would move the agaves now since you are in Southern NM . Unless you are in clay, I don't think rot is a problem You don't have a lot of rain in the winter like they do in California. You also are not that cold. I have moved agaves in winter in Central Texas (8b) and had no problem. I would let them calous off for several days. When I do that, I have no problems.I like to give everything as much time as possible before the big heat hits. Don't water them for several days after planting. Agaves are really tough critters and they probable can be moved anytime and that is why the conflicting info. I have jerked them out of the ground severing all sorts of roots and planted them during the spring and they did well then also.

nmgirl, do Agave grow where you live if so, are they growing now. Are they used to the cold. Some Agave do just fine in the cold, others not so and the leaf ends burn from the cold. Not knowing how cold you get where you live I cannot respond properly, what is the species. I have the Gentry book on Agave, I wonder it it will tell me anything there which I will be able to report back. If they have been doing well along before you moved in I would guess they would do just fine. It may take a little while to adjust to the shock of moving them. Norma

I just dug up and moved some big blue agave that were taking over a flowerbed. We don't have really wet winters or a lot of cold. I've let them dry for a week before planting them and others I've planted the same day they were dug. They are tough plants. I also just planted some agaves from a plant trade last weekend.
Tally HO!

What do you consider hot?

In Arizona it is 90 plus from February. So I assume early may is okay to transplant?

If this is an Agave Americana, they really do not care much. I moved two 10 year olds last year before winter and both are doing just fine out in my yard. Neither one of them had much of a root system either, I just basically tore them out with a shovel.

I have since yanked agaves out leaving most of the roots because the dirt was dried clay. Really ALL the roots were gone. After callusing the cut, I then placed it on a porous soil and did not water them for several weeks till I felt resistance . they grew roots.