I bought this new last month and it has already started giving light buzz on the first two frets especially when I play an Am chord. 

Wondering if this might be because of temperature (i usually keep the guitar in my bedroom at c.20 degrees). I have a 1 yr warranty on the guitar so could potentially use it to fix this.

if the buzz is only on the 1st few frets then your truss rod is probably too tight.
Not taking any online orders.
Yes the truss rod is likely now too tight, resulting in the neck being to straight. Necks often have this kind of instability, where the amount of neck relief varies with climate changes, and some are worse than others. If it is under warranty, then it is likely best to have the shop adjust it, but it is the kind of thing that should eventually be DIY, especially if the neck is particularly prone to change.