values = {1534, 1404, 1484, 1564, 1414, 1464, 1534, 1454, 1414, 1444,
1584, 1534, 1604, 1474, 1554, 1484, 1414, 1484, 1604, 1474, 1484,
1826, 1856, 1806, 1916, 1826, 1786, 1906, 1846, 584, 724, 544, 644,
1409, 1309, 1659, 1389, 1359, 1389, 2400, 1389, 2400, 2650, 3550,
3550, 3500, 1409, 1289, 1559, 1409, 1609, 1409, 1339, 1409, 1609,
2874, 1609, 4000, 4450, 4000, 3770, 4000, 2500, 2650};
mat = Partition[values, 8, 8];

colours = Reverse[{Red, Yellow, Green, Cyan, Blue, Magenta}];
z1bound = 1000;
z2bound = 5000;
colourfunc =
Function[Blend[Reverse[{Red, Yellow, Green, Cyan, Blue, Magenta}],
Rescale[#, {z1bound, z2bound}]]];

ArrayPlot[mat /. x_ /; (x < 1000 || x > 5000) :> White,
 ColorFunction -> colourfunc, ColorFunctionScaling -> False]

ArrayPlot[mat ,
 ColorFunction ->(If[# < 1000||# > 5000, White, colourfunc @ #]&),
 ColorFunctionScaling -> False]