In this paper we study mechanisms that permit to augment the FaaS middleware with support for Transactional Causal Consistency (TCC). At first glance, it may seem that offering TCC to FaaS applications can trivially be achieved, given that the FaaS paadigm does not prevent applications from selecting the storage service with the properties they need. Unfortunately, most TCC storage services ensure consistency only to individual client processes, while a FaaS application is executed by multiple, independent, worker processes. Therefore, there is the need to coordinate the workers, a task that can be a significant source of overhead. We propose a novel architecture to support TCC in FaaS, named FaaSTCC, that significantly reduces the coordination overhead. FaaSTCC achieves this goal by augmenting the workers with a caching layer and by implementing novel mechanisms that maximize the cache usage. First, our storage layer offers to the caching layer a promise, that sets a horizon where the versions retrieved by the cache are guaranteed to be consistent. Second, in FaaSTCC, functions coordinate using snapshot intervals, that support the lazy identification of the read snapshot, increasing the chances of using the cached values. We have implemented and experimentally evaluated FaaSTCC. Our results show that FaaSTCC achieves up to 5x lower average latency and 6x lower tail latency than previous work.