The fastest way is probably to get a taxi. The journey time is 44 mins (though probably a bit more allowing for traffic), but there will be very short wait times at Kings Cross and it will drop you at the door of your Heathrow terminal. The cost is about 75 pounds, which split four ways is not bad: for four adults that is actually cheaper than the Heathrow Express.
The next fastest way is to take a taxi from King's Cross to Paddington and then get the Heathrow Express to Heathrow. Taxi fare is going to be about 16 pounds, which split between 4 people is pretty reasonable. The time is about 20 mins for the taxi (add a few minutes of wait time at peak hours), the express time is 15 mins and the max wait for the express is 15 mins. Add five or ten minutes to get from the station to the terminal and it comes in on average at 60-65 minutes. However for four adults this will be more expensive than the taxi option. If any of your party are children then that changes things - children travel free on the Heathrow Express. This contributes less to climate change, if that's significant for you.
As Michael Hampton points out, the tube direct on the Piccadilly line is going to be much, much cheaper than any of the above, and only slightly longer. The journey is around 55 minutes, with maybe five minutes to get to the underground, a five minute wait and 5-10 minutes to get from the underground to the terminal, it's likely to clock in at 70-75 minutes. Hoever its only a few pounds per person, and is undoubtedly the best value for your pound. It's also the most environmentally friendly option.