How can I make a SQL temp table with primary key and auto-incrementing field?

You are just missing the words “primary key” as far as I can see to meet your specified objective.

For your other columns it’s best to explicitly define whether they should be NULL or NOT NULL though so you are not relying on the ANSI_NULL_DFLT_ON setting.

CREATE TABLE #tmp
(
ID INT IDENTITY(1, 1) primary key ,
AssignedTo NVARCHAR(100),
AltBusinessSeverity NVARCHAR(100),
DefectCount int
);

insert into #tmp 
select 'user','high',5 union all
select 'user','med',4


select * from #tmp