Transformer Efficiency Issue
You haven't mentioned the load current, in addition to Kevin's list of missing information. 

The problem could be : 


primary inductance too low (not enough turns on the primary), 
core saturation (too many turns on the primary) or 
both at the same time. 


Since you can't simultaneously increase and decrease the primary turns, the last of these requires either a higher switching frequency, a bigger core, a different core material, or a combination of all these.

I'm suspecting core saturation because of your comment that heating worsens the problem (you'll probably find core permeability reduces with increasing temperature, reducing the primary inductance thus increasing the current, causing thermal runaway). Does freezer spray reduce the current?

Once the basics are right you can further improve efficiency by (for example) increasing wire diameter if I^2*R losses are important, or interleaving primary and secondary windings if leakage inductance is too high, but you're not at that stage yet.

Better information as Kevin asked will help improve the answers. At least, tell us 


the switching frequency, 
the primary inductance (measure across both legs of primary with secondary OPEN circuit)
the leakage inductance (measure across both legs of primary with secondary SHORT circuit)  


and anything you can about the core.