When you discard a card with madness, instead of going to the graveyard it is exiled — but this exile is not a cost you pay; it is a replacement effect that changes where the card goes (CR 702.35b). The card is exiled face-down in a special 'madness exile zone' state, waiting for the triggered ability to give you the option to cast it for its madness cost or let it go to the graveyard.
Because the card is exiled as part of the madness replacement effect — not as a cost or an action you control on demand — you cannot redirect that exile to satisfy another effect or cost that requires you to 'exile a card.' Costs and replacement effects are entirely separate game actions (CR 117.1, CR 614.1).
Additionally, the exiled madness card is in a specific pending state tied to its triggered ability (CR 702.35c). Using it to pay some other cost would remove it from that process in an illegal way; the rules do not allow a single game object to simultaneously satisfy two different requirements.
Example: You discard Fiery Temper (madness {R}) while Containment Membrane is asking you to exile a card from your hand as an additional cost. You cannot use Fiery Temper's madness exile to pay that cost — the discard-to-exile is a replacement effect on the discard, not a voluntary exile action, and the card is already earmarked for the madness trigger.
The bottom line: madness exile is an automatic replacement effect (CR 702.35b), not a player-controlled cost payment, so it cannot be used to satisfy any other exile requirement.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.