<p>I've read different things about PLA and heat-bed. Some say it is not needed, others recommend 60-70°C, but not for the first layers.</p>

<p>For larger objects I often have the problem that the object does not stick to the blue-painters-tape-covered aluminium print plate. Instead the print "curls" up on one or more corners. To reduce this effect, I'm using a brim between 5 and 10mm. Depending on the size of the object the brim works quite well. Will heating the bed also improve the print quality by reducing the amount of heat warping / curling?</p>

It really depends on your formulation. 70 °C would be on the higher end. I think I do between 70 °C - 75 °C. Not any higher.
Add a glue from a glue stick to help with keeping it on the bed.
Use a raft to reduce the issue as well.
A fan is the number one thing you can do.
The last solution is to build a heat enclosure. They are not on every 3D printer because of patents blocking them. You can easily make your own.
Technically it is not 100 % needed, i.e. the MakerBot does not use it, but the guys at MakerBot have PLA down to a science.
Also I thought Kapton is not for PLA usually... see these
MatterHackers
articles:
How to succeed when printing with ABS
;
How to succeed when printing with PLA
.
From
RepRap Wiki - Glossary
:
Raft
A technique used to prevent warping. Parts are built on top
  of a 'raft' of disposable material instead of directly on the build
  surface. The raft is larger than the part and so has more adhesion.
  Rarely used with heated build surfaces. For the small area models, it
  is very useful to prevent warping via adding a raft for the model
  before slicing it. It can also help with with precision parts by
  removing the slight first few layer distortion caused by the heated
  bed.