The fastest way is going from King's Cross St Pancras tube station to Paddington tube station first via *Hammersmith & City line or Circle line/Circle line* and then interchange to the Heathrow Express at Paddington rail station. The trip takes about [30-35mins][1], plus 5-10 mins from the rail station to terminal 2 and <20mins waiting time (<5mins for tube and <15 mins for heathrow express). The trip costs [£24.5][2].

On the other hand, since you have enough time, I would recommend Michael Hampton's answer. The trip takes half an hour longer but costs only £6 and waits 10mins less.


  [1]: https://www.tfl.gov.uk/plan-a-journey/results?IsAsync=true&JpType=publictransport&InputFrom=king%27s%20cross&DataSetsJson=null&DataSetsJson=null&DataSetsJson=null&Modes=tube%2Cdlr%2Coverground%2Ctflrail%2Cbus%2Criver-bus%2Ctram%2Ccable-car%2Cnational-rail%2Criver-tour&Modes=tube%2Cdlr%2Coverground%2Ctflrail%2Cbus%2Criver-bus%2Ctram%2Ccable-car%2Cnational-rail%2Criver-tour&Modes=tube%2Cdlr%2Coverground%2Ctflrail%2Cbus%2Criver-bus%2Ctram%2Ccable-car%2Cnational-rail&From=King%27s%20Cross%20(London)%2C%20King%27s%20Cross%20Station&FromId=1001171&FromId=&InputTo=Heathrow%20Airport%20Terminals%201-3&To=Heathrow%20Airport%20Terminals%201-3&ToId=1000105&TimeIs=departing&Date=20150617&Time=0600&IsMapRequired=undefined&Mode=bus&Mode=tube&Mode=national-rail&Mode=dlr&Mode=overground&Mode=tflrail&Mode=river-bus&Mode=tram&Mode=cable-car&Mode=coach&CyclePreference=AllTheWay&WalkingSpeed=average&WalkingSpeed=average&JourneyPreference=leasttime&InputVia=&Via=&ViaId=&NationalSearch=false&AccessibilityPreference=norequirements&MaxWalkingMinutes=40&SavePreferences=false&IsMultipleJourneySelection=False&JourneyType=&IsCycleHireOriginOrDestination=False&OnChosenOptionScreen=False&IsPastWarning=False&AlternativeTime=0553
  [2]: http://www.thetrainline.com/buytickets/combinedmatrix.aspx?Command=TimeTable#Journey/LONDON%20ST%20PANCRAS%20INTL/HEATHROW%20AIRPORT%20(ANY)/25/06/15/12/30/Dep//////Dep/1/0//