If you're seeding in the spring you need to wait until soil temperature is at least 50-65 degrees before most grasses will germinate effectively. Even though daytime temperatures may be in the correct range the soil will take time to warm up.
Edit to answer comment and updated temperature:
At this point in the season you've missed the opportunity to reap the benefits of winter sowing. It's the freeze/thaw cycles that give the benefit. As the soil freezes it opens up pores which then close as the soil thaws.
If you put down seed now, before ideal conditions for germination it's going to just sit there. You'll lose some to birds, squirrels and possibly some to frost if you get a warm spell that begins the germination process followed by a very cold day.
You also won't know when the seed starts to germinate which can cause issues with providing proper irrigation.
I think you'll have more success at this point waiting until soil reaches at least 60 degF and is rising with no signs of frost or sub freezing temperatures in the long range weather forecast.