The fire also seems to be green when the person traveling by Floo arrives in the destination fireplace.
“The Atrium was full of people; the floor was reflecting the emerald green flames that had burst into life in all the fireplaces along one wall; and streams of witches and wizards were emerging from them.” - Harry Potter and the Order of the Phoenix, Chapter 36 (The Only One He Ever Feared)*
When Dumbledore arrives by Floo, the fire he appears in is green as well.
“The empty fireplace burst into emerald green flame, making Harry leap away from the door, staring at the man spinning inside the grate. As Dumbledore’s tall form unfolded itself from the fire, the wizards and witches on the surrounding walls jerked awake, many of them giving cries of welcome.
‘Thank you,’ said Dumbledore softly.”
- Harry Potter and the Order of the Phoenix, Chapter 37 (The Lost Prophecy)
#The fire is green (and not hot) for the person making the call.
We get to see the details of how making a fireplace call works when Harry attempts to call Sirius from Umbridge’s office. The person making the fireplace call uses Floo Powder, and sticks their head into the emerald green fire, but the fire on the receiving end remains hot and orange.
“Harry pulled off his Cloak and, striding over to the fireplace, found what he was looking for within seconds: a small box containing glittering Floo powder.
He crouched down in front of the empty grate, his hands shaking. He had never done this before, though he thought he knew how it must work. Sticking his head into the fireplace, he took a large pinch of powder and dropped it on to the logs stacked neatly beneath him. They exploded at once into emerald green flames.
‘Number twelve, Grimmauld Place!’ Harry said loudly and clearly.
It was one of the most curious sensations he had ever experienced. He had travelled by Floo powder before, of course, but then it had been his entire body that had spun around and around in the flames through the network of wizarding fireplaces that stretched over the country. This time, his knees remained firm upon the cold floor of Umbridge’s office, and only his head hurtled through the emerald fire …
And then, as abruptly as it had begun, the spinning stopped. Feeling rather sick and as though he were wearing an exceptionally hot muffler around his head, Harry opened his eyes to find that he was looking up out of the kitchen fireplace at the long, wooden table, where a man sat poring over a piece of parchment.”
- Harry Potter and the Order of the Phoenix, Chapter 29 (Careers Advice)