If I have Elemental Hero Avian (ATK 1000 DEF 1000) equipped with Heart of Clear Water and a Skyscraper on the field, will Heart of Clear Water be destroyed if Avian attacks a monster with an ATK higher than 1000? The ATK increase is during the damage calculation only, so I don't know.

Heart of Clear Water
If the equipped monster's ATK is 1300 or higher, this card is automatically destroyed. The monster equipped with this card is not destroyed in battle or by the effect of a card that specifically designates a target. Battle Damage is calculated normally.

Skyscraper
When a monster that includes "Elemental Hero" in its card name attacks, if its ATK is lower than the ATK of the attack target, increase the ATK of the attacking monster by 1000 points during damage calculation only.

Here's what Upperdeck has to say about these two:

HEART OF CLEAR WATER

You may equip this card to a monster with ATK 1300 or greater, but it will be immediately destroyed.

If a monster equipped with this card has its ATK increased over 1299, by the effect of "Rush Recklessly", etc., this card is destroyed.

If your "Relinquished" or "Thousand-Eyes Restrict" is equipped with "Heart of Clear Water" and you its effect to equip it with a Monster Card whose ATK is 1300 or higher, "Heart of Clear Water" is destroyed.

Your monster equipped with "Heart of Clear Water" is not destroyed in battle, but you still take any Battle Damage that would be inflicted to your Life Points by the attack.

If you Special Summon a monster with "Premature Burial" or "Call of the Haunted" and then equip that monster with "Heart of Clear Water", the monster will not be destroyed if "Premature Burial" or "Call of the Haunted" is destroyed.

A monster equipped with this card can still be destroyed by effects that do not target, such as the effects of "Fissure", "Dark Hole", "Smashing Ground", or "Torrential Tribute".

A monster equipped with this card cannot be destroyed by a card that targets, but it may still be declared a target. So the opponent may activate "Nightmare Wheel" or "Snatch Steal" targeting your monster equipped with "Heart of Clear Water".


SKYSCRAPER

The ATK increase of “Skyscraper” is a Continuous Effect and does not start a chain.

If “Skyscraper” is on the field and you attack a Defense Position monster with an “Elemental Hero” that has ATK lower than the ATK of the Defense Position monster, the “Elemental Hero” gains +1000 ATK even though it was attacking a Defense Position monster.

If your opponent’s monster’s ATK is increased during the damage step, like “Injection Fairy Lily” or “Covering Fire”, your “Elemental Hero” will gain the +1000 ATK for “Skyscraper”.

That ruling answers your question. Even if it's a temporary increase, if the increase happens at all, Clear Water will be destroyed. So if Avian attacks a stronger monster, its ATK will raise to 2000, which is well over 1299, destroying the Equip.

Even with the timing of Skyscraper and the fact that you can't chain to it?

The destruction of Heart of Clear Water does not start a chain, nor add to one. It's just something separate that happens at the moment.

Rush Recklessly could also happen in the Damage Step, and Heart of Clear Water would be destroyed even then because it doesn't use the chain.

technically you could refer to it as a continuous effect that does not go on the chain block. Its always on and actively monitoring the ATK of the equipped monster.

Reason being, HoCW would have to wait for the resolution of a single effect, before destroying itself, but it could interrupt a chain between links if a chain were to initiate in the damage step (ex: P1 activating Rush to opponent activating Rush to Magic Jammer)

thanks for the help. I just wanted to be sure before I tried to use them together.