Replacing elements of a nested list by some value

Another interesting approach:

i = 0;
Map[0 # + (20 + 0.1 i++) &, A]

{{20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 
  20., 20., 20., 20., 20.}, {20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1,
   20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1}, {20.2, 20.2,
   20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 
  20.2, 20.2, 20.2}, {20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 
  20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3}}

ClearAll[miF, rPF, tBF];
miF = MapIndexed[20 + .1 (#2[[1]] - 1) &, #, {2}] &;

or

rPF = ReplacePart[#, {i_, _} :> (19.9 + 0.1 i)] &;

or

tbF = Block[{j = 0}, Table[ 0 i + 20 + 0.1 j++, {i, #}]] &;

Example:

A = {{0.620161, 0.320312, 0.94842, 1.11844, 1.12045, 1.12539, 1.13177,
     1.13142, 1.15048, 1.23244, 0.721388, 0.708943, 0.750067, 
    0.744916, 0.720972, 0.674833, 1.29773, 1.29514}, {0.620161, 
    0.320312, 0.94842, 1.11844, 1.12045, 1.12539, 1.13177, 1.13142, 
    1.15048, 0.721388, 0.750067, 0.744916, 0.720972, 0.674833, 
    1.29383, 1.29514}, {0.620161, 0.320312, 0.94842, 1.11844, 1.12045,
     1.12539, 1.13177, 1.13142, 1.15048, 0.721388, 0.750067, 0.744916,
     0.720972, 0.674833, 1.29383, 1.29514}, {0.620161, 0.320312, 
    0.94842, 1.11844, 1.12539, 1.13177, 1.13142, 1.15048, 0.721388, 
    0.750067, 0.744916, 0.720972, 0.674833, 1.29383, 1.29514}};

miF@A
(* {{20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20.},
    {20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1,  20.1, 20.1, 20.1, 20.1, 20.1,
     20.1, 20.1, 20.1, 20.1}, 
    {20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2,
     20.2, 20.2, 20.2, 20.2}, 
    {20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3,
     20.3, 20.3, 20.3}} *)

miF @ A == rPF @ A == tbF @ A
(* True  *)

Using:

A = {{0.620161, 0.320312, 0.94842, 1.11844, 1.12045, 1.12539, 1.13177,
     1.13142, 1.15048, 1.23244, 0.721388, 0.708943, 0.750067, 
    0.744916, 0.720972, 0.674833, 1.29773, 1.29514}, {0.620161, 
    0.320312, 0.94842, 1.11844, 1.12045, 1.12539, 1.13177, 1.13142, 
    1.15048, 0.721388, 0.750067, 0.744916, 0.720972, 0.674833, 
    1.29383, 1.29514}, {0.620161, 0.320312, 0.94842, 1.11844, 1.12045,
     1.12539, 1.13177, 1.13142, 1.15048, 0.721388, 0.750067, 0.744916,
     0.720972, 0.674833, 1.29383, 1.29514}, {0.620161, 0.320312, 
    0.94842, 1.11844, 1.12539, 1.13177, 1.13142, 1.15048, 0.721388, 
    0.750067, 0.744916, 0.720972, 0.674833, 1.29383, 1.29514}};

A function to replace list:

rep[a_, v_] := MapThread[Table[#2, {Length@#1}] &, {a, v}]

so

rep[A, 19.9 + Range[Length[A]]/10]

yields:

{{20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 
  20., 20., 20., 20., 20.}, {20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1,
   20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1}, {20.2, 20.2,
   20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 
  20.2, 20.2, 20.2}, {20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 
  20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3}}