You have omitted the oxygen that is responsible for combustion. If you will copy this as three steps and not run them together you will be less likely to omit reacts you need PLUS you will not confuse products with reactants.
C6H14(l) + heat ->C6H14(g) (step 1)
2C6H14(g) + 19O2 ->12CO2(g) + 14H2O(g)+ heat (step 2)
14H2O(g) ==> 14H2O(l) + heat (step 3)
Steps 2 and 3 are exothermic as you suggest. Step 2 is a combustion reaction. Step 1 is endothermic.