Blackbody Radiation and Temperature Scaling

A blackbody at temperature $T$ has a peak radiation intensity at wavelength $\lambda_{\text{max}}$. At a wavelength of $2\lambda_{\text{max}}$, the intensity is 40% of the peak value. If the temperature is increased to $2T$, what is the approximate intensity at a wavelength twice the new peak wavelength, relative to the new peak intensity?