Most beers/yeasts will ferment at 13C - it is just that they will do it much more slowly and the more aromatic compounds like "fruity esters" may not be produced in such concentrations at lower temps. However 13 is not a very low temperature. Lager yeast can ferment at temperature as low a 5C. But it tends to take a few months at that temperature to make a dry and crisp beer. The reason most brewers brew at a temp range between (say) 18 - 22C is because it is efficient and produces beer in a week or so.
If the cool/cold temperature was a particular concern then an electrically heated Brew Belt or Brew Mat can be used to keep the fermentation vessel warm. Either by itself or using some form of insulation (blanket/duvet?). I have even seen an old electric blanket being used to wrap and heat a 50L fermentation bin. Some have even incorporated a form of thermostat to try to keep a more even temperature.
IMHO there is no real need to worry too much about producing diacetyl or sulphur containing compounds during fermentation. They exist but usually not in the way we imagine (or are told). For example diacetyl is supposed to be an "off flavour" but plenty of it is used in food flavouring and "butterscotch" is consumed world wide. In fact The Tadcaster brewery makes a point of saying their beer is brewed to have a faint diacetyl nose and flavour. As for DMS and other sulphurous compounds I have yet to smell (or taste) any outside of lactobacillius fermentations - even though DMS has been credited for giving lager its unique taste.
The one important thing I have discovered about beer is that it usually improves with a reasonably long conditioning period. A week in the bottle is IMHO much to short. A more useful conditioning period would be 2 months in a bottle. After that time many "off flavours" initially reported are found to have disappeared