"J-B Weld can withstand high temperatures up to 500 °F (260 °C) continuously and up to 600 °F (316 °C) for short periods. It is designed for bonding various materials and is resistant to shock, vibration, and temperature fluctuations."
I've used it to put a chunk of engine block back on a motorcycle that got ripped off by a drive chain coming off and catching a bolt. Held it from leaks and drove it for a few years after that. I'm not familiar with the glass you use and such, probably best to research first.
Sorry if it couldn't help due to the shards you're talking about. Best of luck mate. It works like mixing two putties together and their chemical reaction does the weld at normal temperatures so you don't need electric/gas machines, just patience to not get it all over you hands, rags w.e