The outside temperature has some effect, but the primary source of energy would be from the sunlight. If there is no cooling breeze either, that could exacerbate the problem.
The heating effect on cars is not down to the glass. From what I have read, it would appear that the presence of glass merely affects the rate of heat rise. One compared cars, buses and vans. The van reached the same temperature as the car, it just took longer.
I also wouldn't expect the ELT to have problems the first time it is exposed to temperatures outside its specifications. It might need several excursions outside the permitted range, before problems can occur. If indeed this is what caused it in the first place.