Short comment:
Try EXEC WITH RESULT SETS and specify the metadata yourself for a proc with temp tables; or use the Script Component as a source and specify the Output columns yourself.
Long comment:
Technically speaking, it is the driver/database you are using in SSIS that would decide the behavior when working with temp tables.
Metadata is an important factor when using SSIS's pipeline components. By metadata, I mean the names of the columns, their data types etc that a pipeline component uses. When designing a data flow, someone/something should provide this metadata to the components that require it.
In most cases, SSIS automatically retreives the metadata. Components that do not connect to a external data source, like Conditional Split etc, get their metadata from the other components they are connected to. For the pipeline components that connect to a external data source (like Oledb source, oledb destination, Lookup etc.), SSIS provides a mechanism to get this metadata without human involvement. This mechanism involves the driver connecting to the database and retrieving the metadata of the output. If the driver/database is capable of returning the metadata, then that metadata is used. If the driver/database is incapable, then you get the errors you are seeing. The rest of my comments are based on the assumption that you are using a SQL Server database in your question.
When working with a SQL Server database in SSIS, typically, we use the native client drivers provided by Microsoft. When trying to get the metadata, these drivers try to get the metadata without actually executing the SQL Statement (actual execution can have side effects; and also, might take more than a few seconds/minutes/hours; and you dont want side effects and long wait times during package design time.) So to get the metadata, the driver relies on the metadata of the actual objects used in the sql command. If the command uses a physical table or view, SQL Server already has the metadata available and can supply it to the driver. If it is a temp table, SQL Server does not have the metadata until it can create the temp table. If using FMT ONLY option, you can use it in such a way to create the temp tables, but avoid any heavy processing/side affects and thus be able to retrieve metadata without penalties. Post 2012, these native client drivers rely on some newer functionality to retrieve metadata than the drivers before 2012. In 2012 and after, the driver uses the sp_describe_first_result_set proc to retrieve metadata. So, whether you can get metadata or not is determined by the ability of the sp_describe_first_result_set proc.
So while SSIS can automatically get the metadata (because of the driver/database), it does not automatically get the metadata in some cases (again because of the driver/database). In cases involving the second scenario, some other process (typically a human) can help the driver infer metadata or provide the metadata to the component directly.
To help the driver, in case of SQL Server 2012 and after, you can use the WITH RESULTSETS clause to specify the output metadata. When this clause is present, the driver will use it and doesnt try to query the metadata from system objects; and thus avoid the error which you would otherwise get. If you are using the drivers that came with SQL Server 2008, you can use FMT ONLY. This option is at the driver/database level.
Another option could be to use a Script Component as the Source and in the Output columns, you can specify the columns/metadata. SSIS would not try to retrieve metadata from the datasource in this case, but would rely on the definitions you provided in the Output section of the Script Component.
As you can see, both options involve a human (or some other process) specifying the metadata instead of SSIS trying to retrieve the metadata in an automated fashion. I would prefer the first option if working with SQL Server and the second option if working with databases like MySql.
