Ther thermal EMF of the shunts can be quite an issue, if both sides of the shunt see different heat loads. A fuse in the path can be an issue here as it may produce significant heat on one side.
Getting low thermal EMF is a quite important parameter for the shunt at high precision, high power.
Many shunts are made from manganin and this material usually has a relatively large 2nd order TC that is not easy to trim / adjust by heat treatment. So even of low TC at room temperature the TC can get higher when going really hot. So the problem can be getting worse even faster than I²