You can set the ColorOrder property of the axes to control the colors of the plotted lines, without having to specify each line's color when it's plotted.
Something like this (here I've reduced the number of for loop iterations by a few orders of magnitude):
format long
%DECLARE VARIABLES
M = 1002;%0002;
w = zeros(M,1);
e = zeros(M,1);
dw = zeros(M-1,1);
de = zeros(M-1,1);
T = [0:1000];%0000];
e(1) = 0.0549;
w(1) = 0.3844e9;
% set the axes ColorOrder:
cmap = flip(autumn(61),1); % yellow -> red, with 61 colors (for 61 lines)
set(gca(),'ColorOrder',cmap)
hold on
for g = 12.0:0.1:18.0
for m = 0:1000%0000
de(m+1) = -(4e41 + (2.e40)/g) * ((w(m+1))^(-13/2)) * e(m+1);
dw(m+1) = -((8.1e41)*(e(m+1)^2) + ((1.2e40)/g)) * (w(m+1))^(-11/2);
e(m+2) = e(m+1) + (de(m+1) * 3.154e7);
w(m+2) = w(m+1) + (dw(m+1) * 3.154e7);
end
e = e(1:end-1);
w = w(1:end-1);
plot (T, w)
% hold on
end
hold off
