A monitoring system for monitoring a state of a fluid in an indoor space including a state of a flow field for said fluid is presented. The system includes an input unit (81), a simulation unit (82), a comparison unit (83) and a state correction unit (84). The input unit (81) comprises a plurality of temperature sensors (81a, 81b, . . . , 81mT) to obtain temperature measurement data indicative for a temperature field in said indoor space. The simulation unit (82) is provided to simulate the fluid in said indoor space according to an indoor climate model to predict a state of the fluid including at least a temperature field and a flow field for the fluid in said indoor space, and has an output to provide a signal indicative for the flow field. The comparison unit (83) is provided to compare the predicted temperature field with the temperature measurement data, and the state correction unit (84) is provided to correct the predicted state of the fluid based on a comparison result of said comparison unit (83). The monitoring system may be part of a climate control system.