fast or slow fuse in transformer
A Current fuse opens above a protected current level  defined by some I*t curve.

A Thermal fuse opens above a protect temperature limit which is appropriate for this. It can also protect appliances that are supposed to get hot like  coffee pot heating pads.

When the current can be 800% during a startup, it is not harmful to the transformer until the temperature rises above it's protected limit.

This would apply to low energy transformers not kW , MW sized devices where faster protection is needed.

Consider these, available in any appliance spare part dealer.
http://www.weisd.com/test/WEISD_TBL_view.php?editid1=NTE8125