The phrase "a large cooler" is correct and usable in written English.
You can use it when describing a cooler that has a significant size, often in contexts related to food, beverages, or outdoor activities.
Example: "We packed a large cooler with drinks and snacks for our beach trip."
Alternatives: "a big cooler" or "an oversized cooler."
Tsuzuki returned to the back room, to re-stock from a large cooler.
I then put them in a large cooler with a couple of blocks of ice.
They join other bodies in a large cooler, all in white bags with red tags, stacked six-high on metal traysalmost to the ceiling.
In the rapids, we were only mildly splashed, and on the flat water sections we sat on a large cooler, feet dangling.
Urine collection tubes were configured to split urine to 3 collection containers: 1 acidified with 6 N HCl before collection at a rate calculated to reduce pH to below 2, 1 acidified every 6 h during collection to pH below 2, and 1 located in a large cooler of ice.
The store had obviously prepared itself for the crowds as it was fully staffed and a large cooler of complimentary (non-promotional) Dasani bottled water was being emptied out and handed to me and the other excited shoppers.
Afterwards, we lolled in deck-chairs, and then our host reached for a large cool-box, pulling out cans of lager.
The Bolivian scheme calls for a large cooling plant at a Pacific port, to liquefy the gas for pumping aboard tanker ships.
For someone running a large cooling, heating or pumping system, for example, turning the power off for a short period will not necessarily cause any disruption.
Thus creating a low-temperature magnet with a weak interaction usually is in conflict with having a large cooling capacity and vice versa.
Over all, most scientists I interviewed said they considered that case more convincing than the one put forward by climate skeptics who invoke a large cooling effect.
