Identifying building thermal model with communication imperfections (data-loss and -corruption) is emerging as a major challenge in deploying Internet of Things (IoT) based building automation systems. Further, the building thermal model is influenced by multiple inputs- cooling energy, stray heating, and weather, leading to a multi-input and single output (MISO) system, compounding the challenge further. This investigation presents an approach for identifying high fidelity, yet simple building thermal model suitable for designing predictive controllers for heating, ventilation and air-conditioning systems with IoT induced imperfections. By construction, the problem of finding the lowest order MISO model is a cardinality optimization problem, known to be non-convex and NP-hard. To solve this problem, we first define an atomic norm suitable to relax the cardinality reduction problem for simplifying the identification. Then the resulting problem is solved by employing a randomized version of the Frank-Wolfe algorithm. The performance of the proposed identification algorithm is illustrated on a MISO building thermal model. Our results show that the proposed approach is more suitable for identifying the lowest order building thermal models with missing and corrupted data due to the network.