WPF Control On Separate UI Thread?

If you are querying the database on every keypress - this is going to cause you some lag when typing fast (or even normally)

You would be better off throttling the request, we use this to throttle on the dispatcher thread.

public static class DispatcherExtensions
{
    private static Dictionary<string, DispatcherTimer> timers =
        new Dictionary<string, DispatcherTimer>();
    private static readonly object syncRoot = new object();

    public static string DelayInvoke(this Dispatcher dispatcher, string namedInvocation,
        Action action, TimeSpan delay,
        DispatcherPriority priority = DispatcherPriority.Normal)
    {
        lock (syncRoot)
        {
            if (String.IsNullOrEmpty(namedInvocation))
            {
                namedInvocation = Guid.NewGuid().ToString();
            }
            else
            {
                RemoveTimer(namedInvocation);
            }
            var timer = new DispatcherTimer(delay, priority, (s, e) =>
                {
                    RemoveTimer(namedInvocation);
                    action();
                }, dispatcher);
            timer.Start();
            timers.Add(namedInvocation, timer);
            return namedInvocation;
        }
    }


    public static void CancelNamedInvocation(this Dispatcher dispatcher, string namedInvocation)
    {
        lock (syncRoot)
        {
            RemoveTimer(namedInvocation);
        }
    }

    private static void RemoveTimer(string namedInvocation)
    {
        if (!timers.ContainsKey(namedInvocation)) return;
        timers[namedInvocation].Stop();
        timers.Remove(namedInvocation);
    } 


} 

Assuming you are not using MVVM, you could easily use this like so in your button click

Dispatcher.CurrentDispatcher.DelayInvoke("UpdateSearch",
       YourMethodThatStartsBackgroundThread,Timespan.FromSeconds(1));

Also worth a note : f you are using 4.5 there is the Delay property on bindings you could look at.