Hotheaded Giant — ruling 1

Hotheaded Giant doesn't check whether you've cast another red spell until Hotheaded Giant enters.

Hotheaded Giant — ruling 2

Although Hotheaded Giant says it looks for "another red spell," there's no requirement that Hotheaded Giant actually be cast as a spell (or be red) for this part of its ability to work. For example, if a spell such as Zombify puts Hotheaded Giant directly onto the battlefield, its ability will still check whether you've cast a red spell this turn even though you didn't cast Hotheaded Giant itself as a spell.

Hotheaded Giant : règles, fonctionnement et interactions (MTG)

Hotheaded Giant is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Haste This creature enters with two -1/-1 counters on it unless you've cast another red spell this turn.

How it works : Hotheaded Giant

Original English text — Wizards of the Coast / Scryfall

#1August 1, 2008· Wizards of the Coast
Hotheaded Giant doesn't check whether you've cast another red spell until Hotheaded Giant enters.
No other card is named in this ruling.
#2August 1, 2008· Wizards of the Coast
Although Hotheaded Giant says it looks for "another red spell," there's no requirement that Hotheaded Giant actually be cast as a spell (or be red) for this part of its ability to work. For example, if a spell such as Zombify puts Hotheaded Giant directly onto the battlefield, its ability will still check whether you've cast a red spell this turn even though you didn't cast Hotheaded Giant itself as a spell.
No other card is named in this ruling.