Why was Shana naked after using Tenpa Josai?
One of Alastor's titles is the "Flame of Heaven." In the Shakugan no Shana movie, we see his true, summoned form as a massive creature completely covered in flames, with the form of a minotaur with large webbed-like wings.



Since Tenpa Jousai uses the body of the Flame Haze as a vessel to contain the existence of the Crimson God naturally anything surrounding the container would be consumed by the intenses flames. Yuji was holding Shana's hand when she activated the summoning and came out slightly charred, but survived with the help of the Azure sustained by the his own Power of Existence.

As for the towel/blanket, it could be something extracted from Yogasa, the black cloak/cape that Shana uses to store things, which is said to be an extension of Alastor.