In fall after the summer heat breaks and wetter/cooler weather arrives.

Best season. I suppose we can say the fall is the best time to grow grass; it has less competition from what is not growing.
But, you can sod at any time as long as the weather permits it to receive adequate moisture and sun and can be given ongoing needs.

A hillside is always a problem to grow grass due to its losing moisture going downhill. But, if the soil has the ability to retain that moisture, then the grass stands a better chance to grow lush.
Topdressing lawns with organic matter every spring....and if it can be considered, every fall.
A good compost can do that. Commercial composted cattle or sheep manure can be topdressed at the rate of 1/2" - 1" over the lawn and allow the worms to take it down.
If a more lush lawn is wanted, a topdressing of grass seed can be given at this time...and watered.
If the hillside is dry, then it might require a more cultivated approach to getting organic matter into it. But, if you treat the topdressing as a spring ritual, every spring, the soil there will responds with grass not losing its zest to grow.

Gerberish is gerberish. TW owns/owned a sod farm, I'd go with his advice on this.

Thanks, goren, but won't that humus just wash right down the hill in the next rain?

If there is sufficient grass to hold any additions of humus then it shouldn't be a problem unless the rain is so heavy that rivulets are formed.
When sod is put onto hillsides, its a common thing to pound in short pieces of sticks...1/2" by 1/2", about 10" long to hold the sod in place while it sets roots.
Such amounts of organic matter might be given the same approach.

For readers who do not believe the additions of organic matter can help a lawn I invite you to read further articles on "organic matter, what does it do for soil'.
Where a soil dries out, even immediately after a solid rainfall, it can be pretty well assured that there is no organic matter in the soil to hold such moisture.

Organics can hold the finances to ransom...it is not cheap.
To that then, I heartily suggest homeowners, who have even a small bit of land that can be given over to a compost pile, do it...do it today. Your lawn, your garden, your peace of mind, will be the better for it.
Aside from helping the environment, it just feels good to put your hands into what you know will be of help to your gardening.

Often, on biways and highways, farmers advertize at roadside sale of sheep manure. The prices are usually less than what you pay at the local nursery. And you can be assured it comes from the farm--not from the locally dug up parking lot.

I'm begining to enjoy your posts goren. Post on.