Heimerdinger, Academy Instructor Assume my Heimerdinger is at a battlefield causing the replacement option to be active. Sprite Fountain - [TEMPORARY] (Kill this at the start of its controller's Beginning Phase, before scoring.) When you play this, play a ready 3 Might Sprite unit token with [TEMPORARY] to your base. [DEATHKNELL] Repeat this gear's play effect. (When this dies, get the effect.) Does my mech token come in with Temporary?

Yes — your Mech token enters ready and with [Temporary], so it dies at the start of your next Beginning Phase.

Heimerdinger's replacement effect only swaps which token gets played; it inherits every modification the generating effect applied to the event. Sprite Fountain specifies the token as "a ready 3 Might Sprite unit token with [Temporary]," so those riders carry over onto the Mech (Rule 375 — its examples cover exactly this: a replaced token still enters ready and still gets Temporary). Same for the token from Sprite Fountain's Deathknell repeat.

Location stays the same too — the Mech goes to your Base where the Sprite would have gone, not to Heimerdinger's battlefield.