buddleia davdii brown leaves (zone 10b)

I bought a buddleia davidii in a 7 inches pot. It was about 3 feet high and in stable condition. i transplanted it in my soil bed few weeks ago. Temp is around 100F here and it will reach around 125F in May. First, the edges of some mostly upper and some lower leaves turned brown. Then whole upper leaves turned brown and curled/crispy. The nursery man told me that roots of this plant must remain cool and well drained. I am sure about well drained but not about being cool. I have got few options for mulching. Peat moss, coco peat, shredded leaves etc. Any clue?

I think this is just transplant shock--unfortunately when the temperatures are over 100 that's a very bad time to plant something so it's hard to say if it'll be able to adjust and recover or not. Mulching it is a good idea--I would not use peat to mulch since when it dries out it actually repels water, I'd try the shredded leaves instead. Or if coco peat is the same thing that we call coir over here then it would be fine too, but definitely don't use the peat moss. If there's a way you can rig up some shade for it that would help it--high temperatures are stressful, but high temperatures plus the sun beating down on it may very well kill it before it can get established so if you can at least keep the direct sun off of it until it gets established a bit that may help it survive. And make sure you're watering it enough but not too much (stick your finger down in the soil a few inches and see how it feels--if it's really dry then you're not watering enough, but if it's wet then leave it alone. If your soil is really sandy you may find yourself having to water it a couple times a day, but if your soil is clay then it may go a few days between waterings.

When I buy plants during our hot season, I generally have better luck keeping them in the container for the summer and then planting them in the garden in the fall when the weather cools down. Even when temperatures are in the mid 80's or 90's and it's very sunny it can be hard on newly planted plants and some of them won't make it, and with temperatures over 100 the chances of success are even less. I don't know your climate very well, but I'm assuming you have at least one season where things are a little cooler? That would be the best time to plant things.

If i can provide shade and mulch, can i move it in a bigger clay pot till temp cools down in september?

If you can rig up some shade for it you could try leaving it where it is. If you hadn't already planted it then I would advise you to keep it in a pot until cooler weather, but since it's already been transplanted your best bet may be to try and shade it and hope for the best rather than stressing it again by digging it up and putting it in a pot. It's hard to know for sure what to do in a situation like this but if you can rig up shade for it then I would be inclined to leave it in the garden. If you can't rig up shade for it then I would definitely put it in a pot and stick that in the shade, I don't see how there's any way it'll survive 100-125 degree temps with the sun beating down on it when it's newly planted.