The ICO redemption process doesn't "claim" the HEAT tokens in a concrete form - it merely confirms ownership of the stakes of the ICO participants in the HEAT testnet and assigns them the HEAT accounts to be included in the HEAT genesis block. After this confirmation period is over on Oct 28-30, the HEAT genesis block is created with the initial HEAT tokens automatically distributed to the stakeholder accounts.
There'll be a clarification period of a few months for any unclaimed stakes, that are assigned genesis block accounts and held in custody by Heat Ledger Ltd until their owners are sufficiently identified.
Exchanges will each have one large stakeholder account, from which they can distribute HEAT tokens to customers who wish to withdraw HEAT from exchange accounts to real HEAT wallets. This naturally can't be done until the HEAT tokens have been created through the genesis block.