A cooler mash tun behaves differently from a temperature-controlled kettle in one specific way: the cooler itself has thermal mass, and an unpreheated cooler pulls heat out of your strike water on first contact the same way cold grain does — on top of whatever the grain itself absorbs.
Why the standard calculation can come in low in a cooler
The strike water formula accounts for grain absorbing heat; it doesn't know whether your mash vessel is a preheated kettle with active temperature control or a cold plastic cooler pulled straight from a garage shelf. For 5.44 kg (12 lb) of grain targeting a 154°F mash (a couple of degrees above the earlier 152°F example, to leave visible room for loss) at a 1.5 qt/lb ratio, the standard calculation says 74.2°C strike water. In a genuinely cold, unpreheated cooler, expect the actual resulting mash temperature to land measurably below that target unless you compensate — the cooler absorbs real heat that the calculation has no way to see.
The standard fix: preheat the cooler first
Before adding strike water, pour in a small amount of near-boiling water, close the lid, and let it sit for a few minutes, swirling occasionally — then drain it before adding your actual calculated strike water and grain. This brings the cooler's own material up closer to mash temperature so it stops acting as an unaccounted-for heat sink during the real strike. Most brewers who mash in coolers regularly find this single step closes most of the gap between calculated and actual mash temperature, without needing to guess at an ad-hoc temperature bump on the strike water itself.
If you'd rather compensate on the water side instead
Some brewers skip preheating and instead strike a degree or two hotter than the calculator says, based on their own cooler's known behaviour from past batches — this works, but it's calibrated by trial and error to one specific cooler, and doesn't transfer cleanly to a different vessel or a colder brew-day ambient temperature. Preheating is the more reliable fix precisely because it addresses the actual cause (cooler thermal mass) rather than papering over it with an arbitrary offset that only happens to work under similar conditions to whenever you calibrated it.
What still moves the number after that
Once the cooler itself is out of the equation, the same variables that affect any mash still apply — grain colder than expected pulls the mixed temperature down (see why did my mash come in too cool), and a thicker or thinner ratio than planned changes how much the strike water needs to compensate in the first place (see what is a good mash thickness). A well-preheated cooler with accurately-measured grain temperature and ratio should land within a degree of the calculator's figure consistently, batch after batch.