Jonathan, for goodness sake, just leave it alone. If you cover it all up with that stuff it will die. Let nature do her job and just be patient. It will get warm soon enough. When it gets hot, the grass will burn and go brown - just like everyone else's, and when the weather cools and there's a shower of rain it will all green up again and be fine.
We can help God with our garden husbandry, but we shouldn't try to BE God.
When your grass begins to thicken up, do it a favour and give it a light trim with the mower set on high, as it grows more, mow it regularly without shaving it too low. Watch and wait in the meantime...... or better still, find another garden job to concentrate on, and that way you will progress faster. How about digging an area to grow some veggies in - or even build a shed, or archway or something.