Can anybody identify this clay?
This is non-hardening plasteline, also known as plastecine. 

For the record, although it is labeled as children’s modeling clay, I do not trust it to be non-toxic. Having worked with exactly this product in the past, I did find it to be great when building seals in damming walls of casting molds. If you want it to be harder, you can cool it / freeze it. This will not harden it, as you are only performing a state change in the oils / paraffins that are used to keep the mass malleable. I would be very cautious of overheating it, as you are likely to generate toxic fumes.