Power requirements, and feasibility for a short high power bursts (very fast heating application)
3.5 kJ is something a capacitor bank can cough up in a short time.  For example, that could be 48 V on about 3 F.  You'd have to make sure the capacitors can handle the high current.  Multiple capacitors in parallel, which is what it will take to get to 3 F anyway, helps with this.

However, there is going to be a lot of loss delivering that energy to a load, especially since it isn't "conductive".  Its not clear whether you mean it's not electrically or not thermally conductive, but either way, it makes this problem difficult.  If you do this electrically, you will need to store several times the energy ultimately delivered to the object.

Heating the object chemically might be easier.  For example, a carefully calibrated layer of black powder should be able to deliver the energy in the short time you specify.  There are probably much better chemical reactants than black powder.  I'm just using that as a example.