Heating a wire with electricity

Just trying to teach myself about electricity so I can teach my kids later

There are so many other concepts in electronics, don't start by teaching them how to heat things with electricity on the first step. 

the battery quickly becomes warm, so I think there are no short circuits

Batteries  should never become warm, if it is getting warm it means there is a short circuit and you are draining more current out of it than you are supposed to 

not only is the wire not heating up, but I licked it and didn’t get a shock. (I blew my multimeter a while ago and haven’t gotten another one yet)

Please get another multimer, licking your battery terminals is defiantly not the way to check if a battery is still powered. And please don't do it in front of your kids.

That all said if you want to still heat a wire try nichrome wire and make sure you have some kind of circuit to limit the current flowing through it. Never ever short two terminals of a battery directly with any kind of wire. Also, heating wire can only help you in cutting the plastic I doubt if it will help in sealing plastic bags 

Joule heating, also known as Ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat.

Before going to the solution of your query, I recommend you to not do this kind of stuff with your young kids, as there are many other methods and kits available in market to teach your kids. The solution of your query is that you need to get some nichrome wire, normally found in heating elements, soldering iron, and a very cheap source is the resistors, you can get nichrome wire from any of these. After that you can wrap the nichrome wire on a paper cutter in the form of coil. Then attach a high power battery or adapter of minimum current rating of 2.0 Amps. Then if you want to seal the plastic bags then place plastic bag and use the cutter you made.  Here I suggest you to visit SSLA and contact with their technical support team for getting more assistance in any of your project work.

Before going to the solution of your query, I recommend you to not do this kind of stuff with your young kids, as there are many other methods and kits available in the market to teach your kids. The solution of your query is that you need to get some nichrome wire, normally found in heating elements, soldering iron, and a very cheap source is the resistors, you can get nichrome wire from any of these. After that you can wrap the nichrome wire on a paper cutter in the form of a coil. Then attach a high power battery or adapter of minimum current rating of 2.0 Amps. Then if you want to seal the plastic bags then place the plastic bag and use the cutter you made.  Here I suggest you visit Sierra Software Ltd. and contact with their technical support team for getting more assistance in any of your project work.