Straining seeds from jam
For a jam, (assuming with fruit solids), be aware that since you will have to force it through a strainer whether you warm it up or not, it will lose some of it's fruity texture. But it will taste the same. It will be easier if you warm it, but do NOT let it get hot enough to steam or bubble. And yes, keep refrigerated.

My reference is 65 years of making my own.