Not Much
You've stated that from above the portals are invisible so they are both facing down towards Earth.
Cold air falls and hot air rises, but because of the way they are facing the hot air will rise through the portal, potentially get stuck by the by the cold air, but even then as hot air rises through the portal to reach cold side, once it goes through it will rise straight back up to it's original hot place.
On the hot side you might get some extra wind current as air rises around the portal. On the cold side you might end up with shelf of snow or ice on the non-portal side of your portal.