nonce – How will mining work after 2140?

The nonce header of a block has 32 bits. The vast majority of the time, none of the 2^32 nonces will result in a block hash below the target. So to continue mining, miners usually change the extraNonce in the coinbase transaction. But what will happen once all the bitcoins have been mined and there is no coinbase transaction anymore? I know this will only happen in 2140, but have we thought of a way to change the nonce range when it will be the case?

Thank you for your help.