if object_id('tempdb.dbo.#mytmp') is not null
drop table #mytmp
go

declare @myothertab table (
col2 varchar(20),
col3 varchar(20)
)

insert into @myothertab
select 'A','B' union all
SELECT 'W','Q'
;

declare @myanothertab table (
col2 varchar(20),
col3 varchar(20)
)
insert into @myanothertab
select 'A2','B2' union all
SELECT 'W2','Q2';

select 1 as col1, col2, col3 into #mytmp
from @myothertab

insert into #mytmp
select null,col2,col3
from @myanothertab

select * from #mytmp

SELECT 1 AS col1, st.IDColumn, st.TextColumn
INTO #fred
FROM SomeTable st
  
INSERT INTO #fred
SELECT NULL, sot.IDColumn, sot.TextColumn
FROM SomeOtherTable sot

(10 row(s) affected)
Msg 8101, Level 16, State 1, Line 5
An explicit value for the identity column in table '#fred' can only be specified when a column list is used and IDENTITY_INSERT is ON.