Eat more protein.
I always have my blood sugars drop if I get too hot. I don't even have to really be doing anything but standing outside and my sugars will start to drop after a short period from the heat.
Also something else that used to really get me badly was hot tubs. I would get in a hottub and within about 5 minutes I would be shaking and ready to pass out - hence the main reason I stopped using hottubs about 7 years ago.
I would try to eat more protein with your breakfast. I would maybe add it too whatever else you typically eat. Say if you have a bowl of cereal on average every morning. Maybe make a bowl of cereal and a scrambled egg and some bacon or something along those lines.
Also you could try snaking on peanuts throughout the day or adding peanuts to your meals - say lunch or eating them on the way to work. Peanuts are a good source of protein and you can get them salty so it can help us out in that area too. They typically won't raise your blood sugar so they are a good snack too have.
I would think that you may just be either not eating enough OR eating foods or meals that are not well balanced. Protein will keep your sugar stable over a longer period of time, whereas foods with high carbs will spike your sugar initially but it is more likely to come crashing down an hour or so later. Also with fats you may see a stable sugar for a while BUT you will get a spike AFTER a few hours.
My first thought is to just ad protein to your diet or more protein. Maybe research foods that are higher in protein and see if there is anything you like that you might be able to fit in. Also there are things like Boost with HIGH Protein. If you are allowed to have drinks that might be something to think of. It has carbs but sugars and fats also so it may be enough to keep your sugars from crashing with all the work and the warmer temps inside. Also they are semi small so you could pop the top and drink one relatively quickly if you needed too.
Take Care,
Lindsey