It's possible I've misunderstood your algorithm or requirement, but this seems like it could be a potential performance improvement:
foreach (string arg in searchWords)
{
if (String.IsNullOrEmpty(arg))
continue;
tempList = new List<T>();
if (dictionary.ContainsKey(arg))
foreach (T obj in dictionary[arg])
if (list.Contains(obj))
tempList.Add(obj);
list = new List<T>(tempList);
}
The idea is that you do the first search word separately before this, and only put all the subsequent words into the searchWords list.
That should allow you to remove your final foreach loop entirely. Results only stay in your list as long as they keep matching every searchWord, rather than initially having to pile everything that matches a single word in then filter them back out at the end.