This is kind of a bug in the way H&H runs, but I have found a way to speed up the game, and here is how I found out.
I started playing this game on my Laptop a couple of months ago, and it played fairly decently, but my laptop would overheat, so I tried using my computer. Unfortunately, my computer lagged a lot while playing, in fact, I didnt bother playing on my computer at all, and just bought a laptop fan to keep my laptop from overheating. [EDIT: I used the word lag wrong, it was extremeley low frame rate while trying to play on my computer, but a very fast frame rate while trying to play on my laptop.]
I recently upgraded my graphics card drivers (for my NVidia GeForce 8600 GT) and the game suddenly had no lag on my computer. It may seem simple, but a lot of people do not have the latest graphics card drivers. I also found out that ANY old drivers (even recent releases) still made H&H lag, so if your game lags a lot, then try upgrading your graphics card drivers to their latest release:
1) Open up 'Run' program and type in "dxdiag" without the quotes
2) Click on the display tab and see what your graphics card is (Nvidia, ATI etc)
3) Type down your graphics card model followed by "driver download" in google
4) Find the latest release of your graphics card driver
5) Download the driver
6) Install the driver
7) Restart your computer
8) Re-download the H&H client and try playing
I hope this works for people, and although this isnt technically a bug, I thought people may look here if their computers lag with Haven and Hearth.