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.
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?
Heated bed definatelly helps with PLA adhesion, it also helps depending the surface, for example PEI offers better adhesion than glass. Another option is to try to overextrude the first layer (125%) and make sure it is squeezed out, so basically you get a wavy effect on the first layer. This should help a bit even in the curly corners. Another thing I have noticed from experience is the PLA itself, not all PLAs are the same so you could try another manufacturer or try your PLA in a friend's printer to see if you get the same effect. Generally on PLA we do not expect any warping, but the reality is that some do have.