Twenty years ago Maldacena, Ooguri and Son constructed a modular invariant partition function for the Euclidean black hole (cigar) NLSM. They also proposed an expression for the corresponding density matrix. This result played a key role in the formulation of the remarkable conjecture by Ikhlef, Jacobsen and Saleur that the Euclidean black hole NLSM underlies the critical behaviour of a certain integrable spin chain. In this talk we critically reexamine the above proposals. The talk is based on the recent (unpublished) joint work with V. Bazhanov and G. Kotousov. ------------------------ Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com to receive the link. (Registration is needed only once).