Halogen bulbs can be run at a higher temperature, but they don't have to be - halogen just refers to the gas surrounding the filament.

The bulbs you are replacing used 40 watts of electricity to mostly produce heat. The new bulbs use 28 watts of electricity to mostly produce heat. Since they're using less power, it's going to be difficult to get them to produce more heat.

If the globes feel like glass, they will be fine. If the globes feel like plastic, they will probably be fine - the manufacturer would have to have made an odd choice of plastic to melt at the temperature the bulb will produce.

If you want to minimize the danger/cost, just put one bulb back and see what happens. Run the light for a while, then poke it with something to see if the globe is soft. Make sure you do not touch the globe with part of your body until you know the globe has not softened.

I went ahead with the replacements. The light is just slightly whiter, but not really noticably so unless you are looking for it, and the globes do not seem to be any warmer than the incandescents are.

Thanks to everyone for the inputs.

Just type Globe Halogen Bulbs into a famous search engine.

You can also get Globe LED bulbs, which are more expensive initially but run cheaper and last about 5 to 10 years.

Putting them in an enclosed space will shorten their life. Or so I have read.

I don't think I'd use halogen bulbs in can lights that weren't designed for them, they do run very hot. They also don't have much of a useful life span, at least the desk lamps didn't.

They might have improved them but I prefer cooler running bulbs out here in the desert. I'd likely change the fixture out if I couldn't put a CFL or LED bulb in it.