The heat from the torch will kill the top growth, but will not at first have any affect on the roots. However, repeated burning of of the top growth will, eventually, cause the roots to use up all the energy reserves those roots have and they will stop trying to grow. Due care when using a torch to do this is necessary so that other, more desireable, plants are not harmed and so that organic material is not set on fire.

Why not just pick all of the pods that you see and then have a bonfire? It seems that picking would be much less of a hassle than burning each one with a torch!? If you choose to apply this control technique, do not become lax. If a few pods burst and seeds have escaped and even one of the morning glory seedlings is allowed to go to flower, you likely will have more seed and more seedlings next year. My neighbor keeps contaminating my perennial garden...hate that plant!

Is it morning glory or bind weed. Many morning glories are annuals. However their seeds can live for years and still sprout later. If bind weed you must attack the roots.

Put a sheet under the seeds if possible then hand pick. Many seeds would fall on the ground by hand picking at this time of the year. Try removing this year before the vines dry. Cut above ground and pull.

Hopefully one would get out there and use that torch on these plants long before they produced seeds. The best time to control any plant you consider a "weed" is before it sets seeds.