I don't think planting it then losing the growth is shock enough to ruin the crop. But it might weaken the plant.
Don't chop off the shoot, mulch it DEEP maybe those nighttime temps won't fry it
I have planted many bareroot berries with a green shoot or two but never in such cold weather.
Where is this weather, you described a warm trend is your ground workable?
If you are really concerned stick it in your fridge (check it every few days)
or plant it in a container until you find out what to do.
Btw what varieties of raspberry did they have?
Theres a Big Lots down the road from me

tripleione,
Your post says little guys.How tall,big or old are the Blueberry plants?If they are young,a year or two old and under about two feet,all the flowers should probably be removed.Then the plant can get bigger and healthier to produce fruit next year. Brady

GreenOrchardMom, the ground has been frozen and dethawed a couple of times in my area (mountains of North Carolina). I picked up the 'Heritage' variety of the raspberry plant, and a 'Jersey' variety of blueberry plant. Not sure if there were more varieties, but they did also have grapes and blackberries for sale. My Big Lots also has a simple outdoor greenhouse for sale for $50... my wife and I were thinking about getting it just to be able to go outside and not be cold (hahah).

Bradybb, I have no idea how old either of the plants are. The blueberry plant's stem is about 5-6" long.

Good varieties!
I would wait for a mellow coulpa nights & plant it with leaves & mulch deep over green shoots.

Which Big Lots??

I'm curious about this Big Lot thing too. Do they always sell plants? And seeds?

I bought some blueberry bushes that were in cardboard sleeves at Walmart several years back when it was still winter. They were super cheap and had a one-year guarantee, so I decided to risk it. There was some peat or dirt around the plants and they were already starting to leaf out a bit, so I put them in a cool bedroom (55-60 degrees) in a sunny window for several weeks, keeping them lightly watered. Then when the weather warmed up, I put them outside during the daytime and brought them in at night. I broke them in to the sunlight gradually, starting with a day of shade, then partial day of sun, etc. When it appeared danger of frost was past, I planted the bushes out. Most survived, and they are now my biggest, healthiest bushes. A few years later, I bought some potted blueberries way early and did the carry out to the deck routine for about 6 weeks again. Success again. On a third occasion I ordered some bushes from a reputable firm located farther south. The bushes did not arrive at the specified time. They finally arrived fully leafed out in early April the day before I was flying out of town for a week or so. The instructions were to plant immediately, so I braved a sleet storm to plant them in barely thawed ground. Temperatures were well below freezing at night yet. About half of them died, and the ones that survived have remained stunted for five years, still not at bearing size. So baby them in your sunniest window, put them out during the day as weather permits, and break them in to sunlight gradually. Plant out after danger of frost is past. I would pick off any flower blossoms until the plant is at least well established in the ground, usually the second season. Maybe leave just a few for taste out of curiosity.
I cannot speak for raspberries, as I haven't tried planting them. Northwoodswis