Trying my hand at tomato growing from seeds

I am tried of getting tomatoes and them not tasting like a tomato. So this year I am starting tomatoes from seeds. They have come up and now I am wondering if I should set them outside to harden. I don’t mean to plant them just set them in the shade and bring them in at night. Here is pictures of them.

These are the cherry tomatoes. And the one below are Rutgers. My Mom said they are the ones that her Mom use to plant.

So should I set them out or not, and what is a good day time temp for them? Today and tomorrow it is going to be in the 80’s I think Friday will be in the high 60’s then after that 70’s.