Temperature manifests itself within quantum field theories (QFTs) and conformal field theories (CFTs) via an identification of points in the Euclidean-time direction, which differ by an integer multiple of 1/T. Today, I will talk about finite-temperature path integrals for general QFTs and for two-dimensional CFTs (2d CFTs) on the compact two-torus. By definition, the latter path integrals are modular invariant. I will discuss why, propose an extension of the modular group from SL_2(\Z) to GL_2(\Z), introduce the notion of modular forms with poles, and discuss general properties of modular forms with and without poles that are defined on the extended group GL_2(\Z). Finally, I will discuss how this extension to GL_2(\Z) may introduce a new source of anomalies/consistency conditions in 2d CFTs (and beyond).