Show different background color for time that InfluxDB field matches a string

I am writing my Nest thermostat’s status into InfluxDB every 30 seconds or so. One of the fields that I’m recording is the status of the thermostat: is it heating, cooling, or off? I’ve already got my temperature and setpoint as time series on a simple graph, but I’d like to include a red background area to indicate the times that my furnace was heating. I can’t seem to figure out how to build that query with Grafana, though. Is this something that Grafana supports? How do I get the right data out of InfluxDB to support this?