What is the quickest way to defrost a vegetable curry without a microwave?

Extract it from the container (run the container under the hot tap to loosen up the edges if necessary) and put it in a saucepan.

Add a little bit of liquid (water, juice from canned tomatoes, milk... whatever would go with the particular curry you have) just to cover the bottom of the saucepan so it isn't getting heated dry.

Put it on the stove on a medium heat.

Use a sharp, serrated knife to saw the "frozen lump" into smaller bits, being careful if you have a non-stick saucepan not to scratch the pan surface (you can saw half way through and then prise the halves apart carefully instead of sawing right through the lump).

Keep stirring and turning the lumps over so all sides are getting heated. As the lumps start to loosen up, keep sawing them up into halves.

Within 10-15 minutes all the lumps will be gone and you can make sure it's thoroughly heated through before serving.

Another approach:

Transfer to a heat-proof bag. Remove as much air as possible, seal bag. Put in simmering water (actually, you can put it in the water as you're heating the water—and you can use hot tap water to start). As it starts to defrost, every few minutes remove from water and using some plastic utensil or the back of a spoon (to avoid damaging the bag) mash it a little to stir it.

This will take longer than throwing it in the sauté pan, but greatly reduces the risk of burning it.

Note that standard Ziploc bags can not take boiling; it's supposedly not a safety concern, but the bag becomes extremely soft and will probably break when you try to remove it. There are sous vide zip-close bags that can take boiling (and so can many vacuum sealer bags).