resettable fuse

What you don't say is how much it has to carry as hold current?. Some polymer fuses will do this, but only the versions rated for perhaps 1/4A continuously, will get the switching speed you require. The closer the continuous current is to the trip current, the slower the response to that trip current. You also don't say whether 'resettable', means self resetting, or with a button?. Remember that you can make a fuse like this act very quickly (or at least get rid of the power to the circuit quickly), by having a thyistor crowbar, operated by an overcurrent detector, which then shorts out the supply, and blows the fuse. This only clears, when the supply is broken.

Best Wishes

True. In fact, I have never used them, and I had just started reading some datasheets when I posted my message.

The fuse needs to hold 0.7 A without tripping. I guess that, as you say, it is going to be difficult to react in such a short time to such a small relative change (1.5 / 0.7 (just 2x)).

I was thinking of self resetting.

Thanks.