if you scroll around other questions you'll see that to get to Kings Cross station you have a number of choices.
You don't really know when you will arrive at Heathrow (from presumably either DFW or Interplanetary?), there can be delays or tailwinds or changes to routing, and you don't know how long it will take you to get off the plane and into the terminal and then the lines for immigration (will the e-gates be working, are you eligible, etc.,) and then from there to you transportation into town.
If you're on time, first off the plane into a jetway (none of those 3 guaranteed) and nobody is in front of you from another flight, and the e-gates work like a dream, and you have no luggage, and you have no issues finding the transportation, and you don't need the bathroom or food, and the timetables are exactly matching you, and you are arriving at Terminal 3 or 2, you might be getting on a train in 20 to 30 minutes. If not, well I could only guess.
If you take the Piccadilly Line Tube you can pretty much expect one hour from Terminal 3 to Kings Cross St Pancras unless something untoward arises on the track or in the system and the Tube goes frequently. You haven't said which day or month so don't know but 7 or 8 am going into London is the peak of the rush hour. You and your luggage will start out at Heathrow with a seat for you and a place for your luggage but unless this is Saturday or Sunday or August, or two weeks before Christmas the tube train will fill as you approach central London. Most predictable for time, cheapest.
Next fastest is the Elizabeth Line from any terminal, significantly more expensive, less frequent, change at Farringdon for one stop on the Tube (easy change within the station) to Kings Cross St Pancras, same as above. Fewer stops, more train like (it is in fact a main line train). Still have the rush hour to deal with.
Much more of a faff is Heathrow Express. It does not serve Terminal 4 at Heathrow requiring a change at Terminal 2/3. Every 15 minutes or so, most expensive unless bought far in advance, faster to Paddington station where you then have to change to tube, a fairly difficult connection, you'll be getting a tube at peak rush hour when it is most chaotic and overcrowded, or bus, slower and very crowded at rush hour, or taxi, very expensive and not always easy to get at rush hour and significantly slower to Kings Cross.
Then you need a train from Kings Cross to Hexham, way up north. If you buy a walk-up ticket it will be expensive. Advance tickets are much much cheaper but require you to use that exact train and time. Hence all the timing concerns above.
Understand that there simply is NO train from Heathrow to Hexham or any northern station. You need to break down the steps.
Sounds complicated but when you look at each step you have a limited number of choices, and they all depend on time.
Don't think of taking a taxi or car from Heathrow to Kings Cross at that time of day. It will cost you the earth and be the absolute slowest.
