You can't push the new value from the Rabbit, but you can probably use some Ajax techniques to load a simple JSON structure with "hum" and other variables, and then update just the elements of the web page with the new values.
https://en.wikipedia.org/wiki/Ajax_(programming)
The Samples\tcpip\rabbitweb\thermo_graph.c program demonstrates sending a data structure in JSON format.
Dynamic C doesn't have a sample program for combining the JSON format with Ajax techniques. There is a sample that predates the JSON support in RabbitWeb, using Javascript generation to update multiple fields on a page without having to reload the entire HTML page: Samples/BL4S1xx/TCPIP/rweb_io_sample.c
I don't think you'll be able to run it on a target that isn't one of the BL4S1xx-series SBCs, but you might be able to look through the components for ideas.