How do I seal my baseboards from drafts?
Wait a minute...  that may be a very, very bad idea. sorry kacalapy.  All I can see is messy carpet after that try.  If this carpet is laid on concrete, then the tack strip is fastened with masonry nails, and if installed properly is chiseled over the edge.  No way caulking is going to seal the gaps causing the air leaks. If your leaks are that bad, then do the right thing. Take off the baseboards, see if you can access the sills, if not,  pull back the carpet, and caulk the gap between the sill plate and the slab. Reinstall the baseboards, then re-stretch the carpet to the tack strip. It sounds like no sill seal foam or sealant was installed under the sills.  There is really no quick fix to a problem like this.  BTW, foam padding and carpet carry and "R" value of about 3 to 5 max.  Carpet is never even considered as an insulating material.