@Thorne provides the obvious solution, but let's go a bit more in detail.
This works in both directions. Too cold and the fermentation does not proceed as the yeast hibernates or dies from shock. Too hot and the yeast starts dying from shock as well as producing substances toxic to other yeast (organic processes are generally quite temperature sensitive).
That said, you are more likely to get a quick fermentation if you run hot, and a slow (or non-starter) ferment if you are too cold.
Yeast requires various nutrients to survive. The most well known to brewers are organic nitrogen sources, as well as sugars. Yeast need simple carbohydrates that they can consume to breed. After the initial stage of reproduction, they require nitrogen sources, vitamins, and other micro-nutrients to survive.
It could be the case that the "grapes" that this brewer uses are mostly simple sugars, which would slow down fermentation as well as increase the incidence of off flavours (requiring longer ageing). This is observable on Earth with the production of mead. Mead is made from honey, which is 78% sugar, and basically nothing else. Mead made without the use of additional nutrients generally requires significant ageing, often on the order of months and years.
You mentioned that the brewer is still using the grapes from home, so unfortunately this doesn't work out for you. I've left it in for you reference if you need an additional reason.
Brewing yeast on Earth is bred to be reliable, produce a well-known ABV value, and withstand the stresses of a highly alcoholic environment. Throughout history, this was done via forced selection, where yeasts that made good alcohol would be re-used. In recent years, labs have bred yeast using various techniques to ensure that they perform well in making alcoholic beverages.
It's possible that the yeast on the brewer's home planet was never commercially cultivated, and the wild yeast did not deal well with the stresses of alcoholic fermentation.
This can be demonstrated by attempting to use baking yeast for brewing on Earth.
Yeast requires a certain pH for their proton pump to keep functioning. The reason this is important can be summarised as "complex organic chemistry stuff", but suffice it to say this is how the yeast absorb nutrients and expels waste product. Generally, yeast like an acidic solution, but not too acidic. Somewhere between 4.5 and 5.5 is generally acceptable. Too low and the yeast can't absorb nutrients properly, too high and the yeast begins to decompose due to attack from hydroxide ions.
High pH is rarely a problem in practice though, as most musts are acidic (from malted barley or fruit acids, as the case may be), and will lower the pH of the water.
Too low pH is the more likely stalling condition, and is why meads have a habit of stalling (honey has an incredibly low pH of 3.5).
In our alien brewer's case, highly acidic grapes combined with a slightly acidic water supply could result in a stalled ferment back home, but on Earth, we buffer our water supply with minerals and try to keep the pH between 7 and 8, and this would fix the problem.
Something to keep in mind is that if fermentation is stalled for too long, yeast cells will start digesting themselves. This is called autolysis. This can result in haze as well as odd tastes in the final product. These will air off eventually, but in general, this can range from "needs more ageing than usual" to "tastes like a tyre fire".