The trick to setting this up is to create the #temp1 table before creating sp2 to avoid any "object not found" resolution error while the query tree is being created. The drop the table.
When sp2 is called by sp1, it will automatically re-resolve it's #temp1 entry to the #temp1 created in sp1.
CREATE TABLE #table1 (......)
go
create proc sp2
as
begin
....
delete from #table1
INSERT INTO #table1
......
end
go
drop table #table1
go
create proc sp1
as
begin
CREATE TABLE #table1 (......)
Exec sp2
end