Here are some pictures of E. 'Foxy Lady' and its short bloom time here in the desert when it is 110 degrees every day and 90 degrees at night now. First picture is around midnight; second is 4 AM; third is 8 AM; fourth is 12 noon. They don't last long but are so, so beautiful!
I got the cactus when it was a little baby on eBay with a bunch of other unnamed ones. Its growing in s/h btw.
The flower is similar to Matucana Minime (looking at Cactiguide.com) but the shape of the plant is different. This on seems to be growing up and not getting rounder. Its a small plant, not much more than 2-3inches high.
Nancy it gets into the 90s regularly but cools down into the 70s at night during the heat of the summer. The address is Decatur but we are surrounded by Atlanta on 3 sides. It is humid here, which is very different that AZ. Just standing outside, maybe strolling around the yard, will cause the perspiration to drip off the end of your nose and down your back. To do yard work in the GA summer requires LOTs of water.
From what I've read, one of the ways Matucana pujupatii differs from M. madisoniorum (with which it is often lumped) is the more cylindrical growth.
See the following at http://www.coronacactus.com/PotM_Aug09.htm
" Matucana pujupatii (Donald & A.B.Lau) Bregmann 1988
Synonyms: Borzicactus madisoniorum var. pujupatii, Matucana madisoniorum var. pujupatii
In close relation to M. madisoniorum, this plant, also coming from Peru (Cajamarca) some still consider to be a variety of M. madisoniorum. Its appearance is very much like that of M. madisoniorum but shows more a cylindrical body shape earlier, does not really show the very fine hairs for that velvet appearance and its flowers are a very bright red with a very obvious fluorescent sheen. This plant also offsets quite readily."
Also several photos come up similar to your plant wwhen you do a Google of images of that taxon.