Delete with a multi-column join?

Howdy! I apologize in advance for the ugly query I'm about to throw
your way....

I need to delete some data from a table based on a multi-column join.
Is there a better way to write this?

delete
from tbldata
where unitID || '_' || variableID || '_' || cycleID in
(select unitID || '_' || variableID || '_' || cycleID from
temp_data_table)

In SQL Server I would just write

delete tblData
from tblData a
inner join temp_data_table b
on a.unitID = b.unitID
and a.variableID = b.variableID
and a.cycleID = b.cycleID

but that doesn't seem to be supported in postgres...

Thanks in advance for you help!

Leon