A heterogeneous Internet of Things (IoT) architecture for remote health monitoring (RHM) is proposed, that employs Bluetooth and IEEE 802.15.4 wireless connectivity. The RHM system encompasses Shimmer physiological sensors with Bluetooth radio, and OpenMote environmental sensors with IEEE 802.15.4 radio. This system architecture collects measurements in a relational database in a local server to implement a Fog node for fast data analysis as well as in a remote server in the Cloud.