I would put them in full sun even younger than that, but I have no idea where you live. The smaller they are, the more likely they are to overheat if the air is too still. Use a fan if necessary. Shade them only if you don't have a fan or you have particularly intense sun. Get them used to the sun gradually over a few weeks if they aren't used to it.

They'll grow faster if you keep them warm, 70F-80F is good, but too hot and they'll just go to sleep. Try to let them cool down to around 60F at night.

By 'propagator' if you mean one of those mini-greenhouse-type contraptions, I would strongly discourage it for the same reasons eluded to above - poor air circulation and increased humidity are not part of a successful Lithops equation.

If you want to use a heater, you should turn it off at night, a large day-night temp. differential is beneficial to Lithops and other succulents' metabolism.

And remember, when Lithops are young, they need more frequent light watering than adult plants, most are too small yet to withstand prolonged heat and drought, I would say that by next spring you can begin treating them more like adults. In the wild, most seedlings do not survive, so keep in mind they need to be pampered to some degree during the 1st 12-18 months.

There is plenty of good advice to be had on this forum, simply do a search for "Lithops seedlings" and lots of reading will come up.

How hot can they stand it? I live in Phoenix and just potted one up and put it on my patio. It will receive no direct sun but temps could hit 110 or more. Loretta

Adult plants can take lots of heat, but it is not so easy for them in a small pot where the roots are contricted and more importantly, will heat up to dangerously high levels.

You may want to try and submerge the pot below ground or into a large container where the soil temps can be moderated. Lithops are dormant at such high temps, they can rot easily if watered.

110F, even 120F, is not a problem for Lithops, but direct sun is a problem on potted plants even at far lower temperatures. Lithops are designed with windows on top to let in sunlight, and partially or completely buried in the soil to reduce water loss. But this design means that they heat up in the sun, and at best can only stay as cool as the soil they are in. Plants in the ground stay cool better because the soil a few inches down is cooler. Even in England it is possible to boil small Lithops when there is no air movement.

When the weather is hot, keep them shaded in the afternoons, possibly all day, and try to keep them where they will get a breeze. Be careful about dark coloured pots or top dressings which will absorb heat. If it is above 100F, chances are they will be dormant anyway, tuck them away in a cool corner and forget about them until the end of August :)

I appreciate the advice. I've had a few of the small lithops but this one is rather large in comparison: ~3" tall by 4" across (split in two parts). The others haven't lasted very long, so I'd really try to keep this one alive. I also have some shelves with plant lights inside; do you think it would do better there? Sounds like I'll need to repot it either way, though, because I have it in a pot with four other succulents that will need water on a regular basis this summer. Darn! They all look great together! Loretta