That's a really weird set of circumstances and nothing obvious springs to mind.
I think i'd start with checking the thermostat which you can do by checking the temperature of the top and bottom rad hoses from cold. Start the car up and as it starts to warm up the top rad hose should warm up a lot quicker than the bottom one, then when the car is up to temperature the thermostat will open and the bottom hose should start to warm up as coolant flows. If they both warm at roughly the same rate then its a sure sign that the thermostat has failed.
I'd also check the water flow valve on the bulkhead. It's connected to one of the two coolant pipes which go into the heater matrix. When the heater is on max hot it should open to allow coolant into the heater matrix. When on max cold it should close to stop coolant flowing through the matrix. You can see it easy enough and should see it's lever sitting in two different positions depending on if you have the heater on hot or cold.
The other thing i'd do is check the carpets in both the passengers and drivers footwells to make sure they're not damp.
