How to set Color range for ContourPlots?

Question

I'd like to set the color range for a set of ContourPlots within a Table.

Please notice that the colors in the uploaded picture aren't the same from one plot to the other, (take a look to the interval [0,2] for example), even worse, some colors (like the yellow one in the 2nd and 3rd plots) are missing sometimes:

The code I'm using is this one:

Table[Show[{
ContourPlot[
  (4(1+10^r*Y^2(-94+255 X^2+178*X*Y-77 Y^2+7(5^r)*2^(1+r)*(5X-47Y)(29X-11Y)Y^2)))/(2+2^(2+r)*(5^r)Y^2(5-83*Y^2+2289*2^(1+r)*(5^r)*Y^4)), 
  {X, -1.3, 1.3}, {Y, -1.3, 1.3}, 
  ColorFunction -> "TemperatureMap", PlotRange -> {-7, 7}, 
  PlotLegends -> BarLegend[Automatic], 
  RegionFunction -> Function[{X, Y}, 
  (1/2)(1-(X+Y)^2+2^(1+r)*(5^r)*Y^2(-5X^2+94*X*Y+16*Y^2))>=0]
]}, RotateLabel -> False, FrameLabel -> {"X", "Y"}], {r, {-1.25, -0.625, 0}}]

EDIT: As suggested, I added a few lines of code BUT the results aren't nice yet, take a look:

Results with: ColorFunctionScaling -> False

(* 1st row: Modified lines *)
ColorFunction -> (ColorData["TemperatureMap", 
    Rescale[#, {-7, 7}]] &), ColorFunctionScaling -> False, PlotLegends -> BarLegend[{Automatic, {-7, 7}}],

(* 2nd row: Modified lines *)
ColorFunction -> (ColorData["TemperatureMap", 
    Rescale[#, {-7, 7}]] &), ColorFunctionScaling -> False, PlotLegends -> BarLegend[Automatic],

(* 3rd row: Modified lines *)
ColorFunction -> "TemperatureMap", ColorFunctionScaling -> False, PlotLegends -> BarLegend[{Automatic, {-7, 7}}],

(* 4th row: Modified lines *)
ColorFunction -> "TemperatureMap", ColorFunctionScaling -> False, PlotLegends -> BarLegend[Automatic],

Results without: ColorFunctionScaling -> False

(* 1st row: Modified lines *)
ColorFunction -> (ColorData["TemperatureMap", 
    Rescale[#, {-7, 7}]] &), PlotLegends -> BarLegend[{Automatic, {-7, 7}}],

(* 2nd row: Modified lines *)
ColorFunction -> (ColorData["TemperatureMap", 
    Rescale[#, {-7, 7}]] &), PlotLegends -> BarLegend[Automatic],

(* 3rd row: Modified lines *)
ColorFunction -> "TemperatureMap", PlotLegends -> BarLegend[{Automatic, {-7, 7}}],

(* 4th row: Modified lines *)
ColorFunction -> "TemperatureMap", PlotLegends -> BarLegend[Automatic],

I'll leave the question open for new comments and suggestions.

Answer 1

The automatic legending gets fed the actual plot range, not the one you specified. So you have to specify the plot range in the BarLegend (plus the manual color function scaling, which must match BarLegend):

Table[Show[{
   ContourPlot[(4 (1 + 
         10^r*Y^2 (-94 + 255 X^2 + 178*X*Y - 77 Y^2 + 
            7 (5^r)*2^(1 + r)*(5 X - 47 Y) (29 X - 11 Y) Y^2)))/(2 + 
       2^(2 + r)*(5^r) Y^2 (5 - 83*Y^2 + 
          2289*2^(1 + r)*(5^r)*Y^4)), {X, -1.3, 1.3}, {Y, -1.3, 1.3},
    ColorFunction -> (ColorData["TemperatureMap", Rescale[#, {-7, 7}]] &),
    ColorFunctionScaling -> False,
    PlotLegends -> BarLegend[{Automatic, {-7, 7}}],
    PlotRange -> {-7, 7},
    RegionFunction -> Function[{X, Y}, (1/2) (1 - (X + Y)^2 + 
          2^(1 + r)*(5^r)*Y^2 (-5 X^2 + 94*X*Y + 16*Y^2)) >= 0]]},
  RotateLabel -> False, FrameLabel -> {"X", "Y"}],
 {r, {-1.25, -0.625, 0}}]

Update:

I didn't include the plots my code produced, because the OP's plots had odd stream lines that the OP's code did not produce. I thought I'd wait to see how my answer was received first. Now that the question has been updated, I can respond to this statement:

The 3rd row of these "Results without: ColorFunctionScaling -> False" I've showed you, gave me the desired result.

In third row, the contour levels and the scale in the bar legend are inconsistent, as one can see by hovering the mouse over the contour lines. This is typical of the case where ContourPlot automatically scales the colors in the plot and the user scales the colors in the legend. It's rare they coincide.