We demonstrate improvements to the cooling power of broad bandwidth (10 GHz) microwave attenuators designed for operation at temperatures below 100 mK. By interleaving 9-mu m thick conducting copper heatsinks in between 10-mu m long, 70-nm thick resistive nichrome elements, the electrical heat generated in the nichrome elements is conducted more readily into the heatsinks, effectively decreasing the thermal resistance between the hot electrons and cold phonons. For a 20 dB attenuator mounted at 20 mK, a minimum noise temperature of T-n similar to 50 mK was obtained for small dissipated powers (P-d < 1 nW) in the attenuator. For higher dissipated powers, we find T-n proportional to P-d(1/4.4), with P-d = 100 nW corresponding to a noise temperature of 90 mK. This is in good agreement with thermal modeling of the system and represents nearly a factor of 20 improvement in cooling power or a factor of 1.8 reduction in T-n for the same dissipated power, when compared to a previous design without interleaved heatsinks. Published under license by AIP Publishing.