Will we even be burning fossil fuels in approx. 100 years? Worry about climate effects?
Based on the stats for the US only, I would say we have the capacity for using fossil fuels over the next 100 years.  Whether or not we worry about it is another discussion entirely.  The US has coal resources for the next 250 years and I suspect may be producing and using natural gas for the next 100 years.

For the US (from the US Energy Information Administration)


256 years of coal resources available (based on 2014 numbers) link
~12 years of natural gas resources available 
Based on resources and current usage rate Link

This is a rough estimate does not take into account importing or exporting natural gas.Also assumes usage based on 2015 numbers.
0 years of oil resources (no surprises here)
US uses 19.4 millions of barrels per day link
US produces &lt;9 millions of barrels per day link    


Here is fun stat laden site for global oil and gas resource and consumption. link.  

Note: I take these stats at face value but oil resource production and reserve numbers are not always accurate.  A number of oil producers are reluctant to provide accurate stats as these numbers are considered sensitive to their economies.