How Do I Avoid This Corelated Subquery?

Hello,
I have a situation which would essentially use a co-related subquery.
I am trying to avoid using a co-related subquery due to its slow
performanc and use a join statement instead.

Here is what I am trying to do:

Tables:
========
Limit
-------
RelID ProdID Days Amt1 Amt2
----- ------ ---- ---- ------
148 2 30 15000 30000
148 2 7 1000 2500

Temp Limits
-----------
RelID ProdID MaxDays Amt1 Amt2
----- ------ ----- ------ ------
148217500 1000
1482717500 500
1482302500 2000
14829025000 750
14821807500 -300

I want the totals of Amt1 and Amt2 in the TempLimits table added to
each row in the Limits table where the Days in the Limits Table >=
MaxDays in TempLimits
So, when I run the query with the above data
I need to get

RelID ProdID Days Amt1 Amt2
----- ------ ---- ------ ------
148 2 30 42500 (15000+7500+17500+2500) 33500
(30000+1000+500+2000)
148 2 7 26000 (1000+7500+17500) 4000
(2500+1000+500)

************************************************** **************************
Here is the query that I have right now...

update Limit
set Amt1 = isnull(Amt1,0) + IsNull(temptable.temp_Amt1, 0)
, Amt2 = isnull(Amt2,0) + IsNull(temptable.temp_Amt2, 0)
from Limit inner join
(
select Templimits.relationship_id relationship_id,
Templimits.product_id product_id, sum(Templimits.Amt1) temp_Amt1,
sum(Templimits.Amt2) temp_Amt2
from TempLimits
WHERE TEMPLIMITS.MAXDAYS <= LIMIT.DAYS
group by limit.relationship_id, limit.product_id
) temptable
on Limit.relid = temptable.relid and
Limit.prodid = temptable.prodid

************************************************** ****************************
As you would see here, I am trying to use the condition for Days
(listed in the query in CAPS) inside the inner query which would not
work... Is there any way I can do this apart from using temp tables
and co-related subqueries?

Thanks in advance
Kannan