There are many methods. It depends on what component of fire risk you are interested in. It could be fire weather, fire hazard (the vegetation component), fire danger (vegetation+terrain+weather=fire behaviour), burn probability, or the combination of all these, i.e. fire risk, which should also consider values at risk or potential damage.

Thanks a lot I have very preliminary concept, however the idea is .... fire risk in response to climate change (increase temperature and .......) could you please help further?

You will find plenty of papers on the subject:

http://scholar.google.pt/scholar?hl=pt-PT&q=climate+change+fire+risk&btnG=&lr=

Many many thanks

You may use satellite images with GIS to assess the area with dry vegetation prone to catch fire easily and temperature of the area.

Yes, thanks.