I think it is the points not being in monotonic order in T4, and sorting them first will fix it, like you say.
% T4 values to use, in order:
T4_order = 180:240;
% create a random permutation of those values:
T4 = T4_order(randperm(numel(T4_order)));
% calculate the corresponding y values:
y=(1.236*10^(-12))*exp(0.01189.*T4);
% plot (should have the same problem as your plot):
figure();
plot(T4,y,'r');
% sort the T4:
T4 = sort(T4);
% calculate the corresponding y values:
y=(1.236*10^(-12))*exp(0.01189.*T4);
% plot (should be good):
figure();
plot(T4,y,'r');
