Is it possible to upgrade the graphics card in modern laptops?

"To Answer each of your questions below.

A. What expansion slots would the laptop require to do this?

There are a small number of standards for doing this, but this is the minority of laptops and hardware manufactures.

http://www.tomshardware.com/reviews/vidock-expresscard-graphics,1933.html

B. How can you find out if a motherboard/chipset supports upgrades?

It is fairly unlikely but you can use the article above, or contact your manufacture directly.

C. Is heat an issue?

If you are upgrading to a more powerful card, and it is not approved by the manufacturer, I would be careful doing this, and monitor temperatures.

D. Could it void the warranty?

It is dependant on the specific terms of the provider, and if it is not an approved process, I would assume yes.

E. How is battery life affected?

If it is a more powerful card, it will use more battery

This experince comes from owning 2 dell precision laptops, both with quadro graphics cards. The card went in one of them and I had a guy out the next day, who took 30mins to replace the card with no soldering etc.

However, I would assume that finding an upgrade card, may be more difficult, and is not a supported user upgrade."

The short answer is, for the most part, NO. Most modern laptops have the graphics card fully integrated into the motherboard and can't be upgraded without replacing the entire motherboard. For what this would cost in parts and labor, it would almost be cheaper to buy a new computer. There are however, some very high priced laptops that do have dedicated graphics cards that can be removed and upgraded. But these are the exception, not the rule.