Assuming you talking alcohol/ methanol burning engines that are cooled by air and fuel you really won't end up running lean without running hot unless your LSN is way to rich and your HSN is to lean. But the result of which would be bog on the bottom and flame out on top. Generally speaking when your talking gas ratios you can be lean and not run hot. For most fuels they burn hottest at or near their Ideal gas ratio. Methanol's gas ratio is 6.42:1, so it burns hottest at about ~6.3-6.5:1. But at 7:1 (leaner) and 6:1 (richer) the combustion is colder due to incomplete combustion. So in your street car or a water cooled race car you alter fuel ratios and timing to get better fuel economy on the far side(lean side) of stoichiometric. But with the cooling needs of the IC engines running air cooling and methanol based fuels in 2 cycle engines you will either overheat due to lack of cooling(the unburnt fuel is used for cooling) or seize due to lack of lubrication when your air fuel gets to lean.
hope this helps.