In this work, we consider the problem of a general definition of temperature in non-canonical steady states, and review the properties of the fundamental inverse temperature βF of a steady state ensemble where the microstate posterior distribution is a prior times a likelihood function that depends only on the Hamiltonian of the system. We postulate that this posterior distribution is the only family of steady states where temperature can be consistently defined, and provide several consistency checks showing that the definition of βF works as a genuine temperature with interesting properties outside of the canonical ensemble. Within the framework of superstatistics we can interpret βF as the conditional mean of the superstatistical inverse temperature β over a surface of constant energy. Additionally, we obtain a formula that connects the variances of β and βF.