at this movement, we don't have the budget to go higher version, we are planning to use temporary_tablespace and make it default and then try to release the space from tempfiles.
Another option if you cannot change the workload, Free Local storage (temporary files storage), is twice the size of RAM of your Aurora instance. e.g. r5.db24xlarge will provide 1500GB of free local storage. not sure if its possible, but higher instance size may help but that comes with higher cost.