I hope @everephebe doesn’t mind me weighing in on one aspect of his comment. As he said, you can verify whether your tempering efforts have paid off by dipping a scrap of paper in the tempered chocolate and then setting it aside to observe the drying process. But it’s essential that you not put the dipped paper in a cold environment while it’s drying.
One big difference that tempering makes is in the drying speed of the chocolate. Untempered chocolate takes a very long time to set at room temperature, while tempered chocolate sets readily in normal room temperatures (<75 degrees). Your dip test will reflect this. If the chocolate on the paper is actually tempered, you will see unmistakable signs of drying within 2 minutes. If you’ve missed the mark with your tempering technique (a frequent occurrence), you’ll know because after 3 minutes or so the dip test will still show no signs of drying.
Putting the test in the fridge or freezer will deprive you of this valuable indicator, since even untempered chocolate will set quickly in the cold. What’s more, it will cause much of the chocolate on the test to set in the unstable “gamma” crystal form even if it is properly tempered.
Keep in mind that tempering is fussy work. Just going through all of the prescribed steps is no guarantee of a good result. That’s why you have to do the dip test at the end, no matter how good you are tempering. If the test dries quickly and has a smooth satin sheen, you’re good to go (work quickly though, because your tempered chocolate will soon thicken radically in your bowl and reheating it has to be done with care as you risk going out of temper again). If the test is slow to set, or looks funky once it does, then just rewarm the chocolate and repeat the tempering process. You can do this as many times as necessary.