MEMORY_OPTIMIZED table as replacement for temporary tables
In your case, you'd have to use a memory-optimized table variable, and assuming that the child procedures are called by the same SPID, there shouldn't be an issue with visibility. Please see this link:

https://docs.microsoft.com/en-us/sql/relational-databases/in-memory-oltp/faster-temp-table-and-table-variable-by-using-memory-optimization

I will caution you that the cardinality estimator still assumes 1 row for memory-optimized table variables, and this can be an issue for performance. 

More info at this link:

https://blogs.msdn.microsoft.com/psssql/2017/05/10/memory-optimized-table-variable-and-cardinality-estimate/