Well Chris, I don’t know how to do it but based on what I know about how the Ecobee3 works you will need to do one of couple of things depending on the circumstances.
First, I would assume the room in question will be occupied during this particular time frame. If that is the case then the follow me feature available on the thermostat should accomplish what your looking for. The whole idea behind that feature is to use the sensor in the occupied room to decide if the system should ask for AC or Heat.
However, if that isn’t sufficient to meet your needs then it seems to me you will somehow have to the decision making process out of the hands of the thermostat. That’s the part I don’t have the experience to help you with. Lot’s of smart people in this community though. If I’m not mistaken there has even been a custom device handler written for the ecobee3 though I’m not sure what additional capabilities it might expose.
Take a look here and see if it helps.