Cryogenics refers to the study of materials at very low temperatures, below -150C
So you can't really do cryogenic experiments at home, however, you can do some simple experiments comparing the strength of different metals at a variety of temperatures which you CAN accomplish.
So, for example, -20C, 0C, 20C, 100C
And remember to define strength, I would suggest an experiment using a thin beam of a variety of metals, such as iron, stainless steel, magnesium, alluminium, supported in a clamp stand, and measure the beam deflection with a specific load attached to one end.
So, your measurements would be, for example, bend in mm with a 1kg load, with a 250mm x 5mm x 5mm metal beam.