In order to analyse complex networks in the cerebral cortex, different approaches are used in computational neuroscience: microscopic network models that consider every single neuron in simulations aiming for a realistic biological description as well as heuristic firing rate or neural-mass models which deliver a simple macroscopic description. Recently, a stochastic mean-field model that describes the coarse-grained dynamics of generalized integrate-and-fire networks at the intermediate mesoscopic scale has been proposed [1,2]. The mesoscopic model accurately accounts for both single neuron dynamics and fluctuations due to finite network sizes. However, the theory is based on the assumption of homogeneous neural populations and all-to-all connectivity – assumptions that are not fulfilled in biological neural networks. We present a mesoscopic model derived for a microscopic network of heterogeneous Poisson spiking neurons with random connectivity and synaptic delay. The randomness of the adjacency matrix is quenched, i.e. fixed for each trial. For the analytical treatment of the quenched randomness we use an annealed approximation, where a new adjacency matrix is drawn whenever a spike occurs in the network [3]. This approximation allows us to derive a system of Langevin equations for the membrane potentials that are driven by a common finite-size noise due to the Poisson spiking and an independent white noise capturing the quenched randomness of the connectivity. Using a Gaussian approximation, we further derive a three-dimensional Langevin model for the conditional mean and variance of the membrane potentials at the mesoscopic scale as well as a variable describing the finite size fluctuations of the average firing rate in the population. The resulting mesoscopic model is characterized by an effective transfer function that is flattened by the instantaneous voltage variance representing the effect of the quenched randomness of connectivity and heterogeneity. This flattening theoretically and quantitatively explains the stable asynchronous activity in simulations of random networks, for which a naive mean-field approximation would incorrectly predict strong synchronization. The flattening also explains a reduced variability of the firing rate for an increase in an external noisy coherent current which is not present in a naive mean-field approximation. The theoretical predictions are in excellent agreement with extensive microscopic simulations.