Why Styrofoam melts in kerosene?

Your first question is wrong, unless you have heated your kerosene, the styrofoam does not melt, it dissolves.

Second question... It depends. The solubility of one thing in another thing varies with temperature. Typically, the solubility increases with increasing temperature but there are exceptions. If you want to know the max solubility for styrofoam in kerosene at STP, you may be able to find that in chemical handbooks.

probably for the same reason it melts in gasoline:

Like polystyrene, the compounds found in gasoline are all very nonpolar, meaning electrons are equally shared in bonds in the molecule so there aren't any partial charges. Styrene includes lots of aromatic groups, and gasoline contains some aromatic compounds like toluene and xylene. A general rule is that "like dissolves like," and gasoline can indeed attack Styrofoam. Kerosene will do likewise. You wouldn't want to store gasoline in a Styrofoam cup anyway because it evaporates readily as it's quite volatile and is highly flammable

Natural ones I didn't know about were

Eucalyptol, which is found in eucalyptus, rosemary and bay oil, can dissolve Styrofoam; the oil cymene, which is found in thyme, can do the same.

It does NOT melt, it dissolves.