Converting a battery powered pocket heater into a portable 5V power source
This will be more complicated than you envision.  USB power is nominal 5 V.  Your battery is less than that, apparently 3.5 V from what you say.  That makes some sense, and makes the charging circuit fairly simple.  The heater is almost certainly designed to be powered directly by the battery.

The problem is that now want to have the unit produce 5 V instead of when it would be running the heater.  This is possible, but will require a switching power supply called a "boost converter".  This steps up the battery voltage to 5 V and also regulates the 5 V.

You might be able to buy a off the shelf DC-DC converter that can take the battery voltage in and produce 5 V regulated out.  If you can find such a thing, that will be the simplest solution.  If not, you could make your own boost converter.  Get a off the shelf chip to help with that.  Unless you are familiar with this stuff (and if you were you wouldn't be here asking), you'll avoid a lot of aggrevation by getting as much of the solution taken care of for you as possible.  A few $ can save hours of frustration.