It all depends on what happens with the temperature. For example, on an ISA day the machine I fly will TAS at 513kts at M0.85 at FL300 (crossover ALT). Keeping ISA we get we get 490ish at FL400 at same Mach speed, or 500ks at ISA plus 10.
Cost index is used to optimise cruise ALT. Disregarding winds aloft, A higher cost index will result in a lower cruise ALT, with faster TAS and higher fuel flow. A lower Cost index will increase the ALT to minimise fuel flow and result in a slower TAS.