You can find links to several other similar questions on cracked granite countertops right below this answer.
While it is possible, I would say ahot pan would only crack a stone countertop if it was one of the very thin ones being sold now (3/8 inch or less), or if it was stressed and ready to crack anyway.
You say it is directly across from the cooktop - I presume you mean at the narrow part of the cutout that goes around the cooktop. Cutouts like this, along with turns of direction of countertops (angle joints or turns),are probably the most common place for cracks by far, because it is narrow and therefore any deformation or settling induces higher stresses in that narrow area. That is why when I do countertops of brittle materials (as opposed to laminates or formica) I use a 3/4" (preferably marine) plywood base under it to support it - and make its fasteners so the 3/4" plywood can be relevelled and reshimmed, thereby relevelling the countertop or tile above it in the process even though it is firmly attached to the plywood.
It can be epoxy filled/glued. Gluing or filling alone may or may not stop it but your odds are not good - to address the situation properly it may need to be removed and re-leveled to relieve any stress in it from bending, which commonly occurs due to settlement/sagging of floors under the weight of the new cabients and countertop.
Get a countertop company with good reviews and reputation to look at it and give recommendations - and you need an expert, not some handyman or such, because done wrong can cause it to snap the rest of the way across. Actually, in some cases that is what is done - breaking it the rest of the way, then epoxy gluing it back together tight to close up the crack, relevelling and remounting one piece of the countertop in the process.
