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.

Without being specific about makes/models the simple answer is ask your supplier.

If they support it, there will be a slot/hatch somewhere on the case that allows access to the graphics card. If it's supported by your supplier and there is a slot for access, no it won't void your warranty. If it's not supported, opening the case will.

That said, I haven't come across any that allow this kind thing. Most laptops are largely propriety hardware because have to be shaped carefully to fit in the case. Most I've used have the graphics processor built directly onto the motherboard. I believe there are a few that it can be done on though.

There's a list of laptop graphics card repair guides here. (Note that anything that requires you to open the case will void your warranty)