Will my grass seed grow in June?

Two weeks ago, I applied Weed and Feed and burned my lawn in many spots. I can't stand the sight of it, so I headed to Lowes tonight and grabbed some Scott's Heat Tolerant Blue Mix and Scott's Starter fertilizer. I plan on removing the dead grass, aerating the soil using a Garden Weasel, applying the seed and fertilizer, then covering the seed with straw. My only concern is, with it being June, is it too late to expect results? I live near St. Louis, MO and the weather here is supposed to be mid 80's for the next week. The Lowe's assistant told me the seed would hold up, providing I water it sufficiently and keep it covered. Is he right?