Sikadog,
I had exactly the same problem when I got my first rifle and was told the following.
For hunting purposes 90% of your shots will be from a cold barrel. Thus next time you shoot a group take a thermos of tea.
Fire one shot from a cold barrel.
Poor out a cup of tea
Fire another shot
Drink a cup of tea
Fire the third shot
By leaving the barrel to cool between shots you should find that our rifle consistently groups its first shots in the same place.
Most sporter weight barrels will shoot differently when hot and cold - it is a simple function of no manufacturer can absolutly 100% ensure that the barrel is exactly concentric, thus it will tend to warp as it heats up.
Key is the first shot position. If a rapid 2nd and 3rd shot is needed most rifles will put that close enough to do the job.
Heavy target barrels, having more metal to them are stiffer, and take longer to heat up, hence they tend to be used in target / varmint rifles where a number of shots need to be taken in a short time frame.