You need to check the coolant level in the radiator directly with the cap off - not the overflow tank. This has all the symptoms of low coolant level, but you need to top off the radiator directly, possibly multiple times. I have had this happen on both Odys and my accord, both times low actual coolant level in the radiator / system. On my '07 Ody, I can leave my garage with the van cold soaked at ~19 F temp of 0F outside and will be getting warm air out of the vents within 60-90 seconds of driving. The thermostat does not need to open to send warm coolant to the heater core. The thermostat opening sends the coolant flow through the radiator (to cool it down). If your level is good, then check the coolant flow valve on the firewall and make sure it is opening the whole way and is not obstructed, and then heater core blockage as noted. But I would start simple.