Here you go:
l=3;
t=linspace(0,1,365);
fun3= @(v) integral(@(v)exp(.071*v),0,v,'ArrayValued',true);
for i=2:length(t)
for j=i:length(t)
xx=t(i);
yy=t(j);
fun = @(x,y) exp(0.14*0.00607*fun3(yy)).*exp(-(x-y).^2/l).*exp(0.14*0.00607*fun3(xx));
y(i,j)=integral2(fun,t(i-1),t(i),t(j-1),t(j));
end
end
It works, but it is very slow.