heatspreaders can in theory improve cooling, but at least as of several years ago many of them were attached using crappy paste that didn't transfer heat well. The end result was many heatspreaders actually trapping in heat. (AKA haswell & ivybridge fiasco

)
The only heatspreaders that might help noticeably are the ones that increase surface area near the path of airflow (the ones with the fins on top). Thus, only the ridiculously tall heatspreaders (which might conflict with CPU HSF).
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RAM typically doesn't use enough power (given it's size) to require additional cooling. In some cases, such as overvolting/overclocking DDR2 or RDRAM might benefit from it, but I doubt it. It's hard to find any actual data supporting/refuting the benefits of heatspreaders

.
http://www.tomshardware.com/forum/247520-30-voltage-damages
michiganteddybear's post describes how power works in ram.
Historically given that RAM size/shape hasn't changed much (since DDR1 took hold anyway), DDR3 is more power efficient than DDR2 (it was heavily advertised as such), and DDR2 is possibly more power efficient than DDR1 (given its use in notebooks at DDR2 400 vs DDR 400). Heatspreaders weren't as common on the original DDR (and none of these were commercially available with the heat fins; I think it started with GSKill/Corsair Vengeance DDR2). I don't even remember them existing on SD (I guess they started out with RD/Rambus based on Tsavo's post). Thus, it's unlikely heatspreaders are actually required (except on RDRAM).
note: RAM voltages have decreased over time, amount of current unknown (but possibly constant). Manufacturing process sizes decrease over time, and likely provide similar efficiency benefits to CPU/GPU die shrinks.
note 2: the samsung ddr3 1600 (30nm) is known to be an AMAZING overclocker and DOES NOT come with a heat spreader.
http://www.techpowerup.com/reviews/Samsung/MV-3V4G3/4.html - test setup shows no heat spreader on samsung (heat spreader w/ fins on GSKILL)
http://www.techpowerup.com/reviews/Samsung/MV-3V4G3/6.html - overclocks to 2400
thus,
TL/DR: imo, based mostly on "educated guessing," heat spreaders are mostly a gimmick and provide no performance benefit [to any ram other than RDRAM *based on info from Tsavo (thanks!)] (other than some people thinking they look awesome).
The TV Series: Futurama said:
Cubert: Hey, Leela, help me apply these flame decals I got in my cereal. They'll make the ship go faster.
Leela: And what's your scientific basis for thinking that?
Cubert: I'm 12.