Some elements of meta-gaming are unavoidable.
Certainly true.
Likewise as far as your character is concerned fire hurts like hell, however the player will usually just see 1d6 per round and think "I can take this for 20 rounds. I just ignore the fire."
However, you've got this one backwards. As far as your character is concerned, fire does 1d6 damage per round and is not especially painful. However, you the player - in whatever capacity - know that real world fire is dangerous and painful and so imagine that the fire has those properties for your character even though it clearly and unmistakably doesn't. Likewise, you are suggesting that the player metagame by playing the character in a way that isn't justified by game reality - as if the fire had the properties of out of game fire rather than the properties it actually has in the game. The problem here is that there is a certain degree of verisimilitude to reality you wish your game to have that the mechanics fail to have. However, the in game world is defined by whatever it actually simulates, not by what you wish it would simulate (what you the player wish was happening in game is inherently part of the metagame). A group that ceases to pretend that the game has features it doesn't have, has stopped metagaming rather than started metagaming.
Now note, I'm not suggesting this is necessarily good for the group. By agreeing to metagame that fire is particularly hot and deadly, the group may have been able to ignore problems with the rules that otherwise would have greatly irritated one or more players. In this case, metagaming is 'good' - if perhaps not the most appropriate solution to a problem that isn't actually occurring in the metagame (how the game is played) but with the game itself (what the rules of the game actually are).
If in fact you want the players to play their characters as if fire was especially painful and dangerous, the best approach is to make fire mechanically have those consequences. Then the game reality will produce the behavior that you desire in the metagame. Asking the player to ignore the game reality in favor of your out of game understanding of fire is asking the player to metagame.
A common example, in 3e especially, was the '5 minute adventuring day.' Having depleted their spells character would often hole up in a room and rest for 23 hours in spite of the fact that they had only fought two battles and spent 10 minutes of their day actually doing something. This is because they saw a sharp fall off in combat effectiveness without those spells slots and so would just refuse to fight. So they would shut a door and pretend to not be there, trusting the GM to let them get away with it in spite of the fact that they are in a castle full of intelligent humanoids and incorporal undead. And the GM, not wanting his game to end, would run the NPCs like mindless drones who ignored the shut door and piles of bodies and the cycle of meta-gaming complicity was complete.
Again, the players aren't metagaming here. The game reality that the characters observe is if you hole yourself up in a room, you are safe and can recover full combat effectiveness. Since this is the most effective in game strategy, this isn't metagaming. It's what actual characters in the observed game world would logically do. The person who is actually metagaming here is the GM, who makes the decision to run intelligent creatures as mindless drones for a reason that exists only at the metagame level - his personal desire for the game to not end.
A player that tried this in my game based on the metagame assumption that monsters don't act according to their recorded intelligence because the GM is afraid to kill PC's will be disabused of that notion quite quickly.
One of the reasons that I, personally, hate x/day abilities is that they encourage meta-game thinking
I think my biggest problem with such powers is rather a different but related problem; namely, that such mechanics are usually dissociated from the game reality and lack a rigorous explanation in the game reality. Usually, if the power is somewhat of a supernatural character, you can invent some plausible association between the mechanics and the described game reality. But x/day abilities that lack a supernatural explanation are just about impossible to associate with the described game reality, because we don't observe abilities having those precise restrictions in the 'real world'. Dissociated mechanics undermine or ability to role play the game, since the game is less and less encouraging us to simultaneously play the game and imagine the reality it is simulating. The more dissociated your game mechanics, the less like a role playing game it will feel to many people.
