Finding Value Of One Column Associated With The Max Value Of Another Column

I've got a rowset (intermediate result in a large query) that's equivalent to this table:

create table T (

K bigint,
V bigint,
W tinyint,
primary key(K,W)
)

What I want is "for each K, find the V associated with the largest W". Or,

select K,V from T t1 where W = (select max(W) from T t2 where t2.K = t1.K)

What I'd like is a solution that does not involve a self-join on the table (which the sub-query effectively is). The rowset can be sorted by (K asc, W desc), in which case I'm looking for the first (K,V) pair for each unique value of K.

In the larger query, T could have 100's of thousands of rows, and as I mentioned, T is the result of another query on my base tables. I can express T as a CTE easily enough, but the resulting query plan (using the sub-select, as above) ends up performing the query that generated T repeatedly in order to implement the self join.

I can save T into a temp table - in fact, that's what I'm doing now - but I'd rather avoid using a temp table if possible. This query needs to be of the highest possible performance, so if there's a no-temp-table, no-self-join solution, I'm all ears!

I could imagine making a CLR UDF that does the filtering that I want, but I'm not convinced that it'd be a good choice - any insights on whether that's worth trying would be appreciated as well.