I don't really fancy accurite things because I found them to be way off, but I've had in the past where one was accurate, so it's a hit or miss thing. Instead I found these digital temp and humidity things on amazon for around $5-7. They're accurate as far as the three that I've used.
A 100w bulb will easily give a hotspot of 95+ degrees. Ideally you would want a hot spot in the upper 80's, and with a 60w you should be able to do that unless you live up north and maybe the room gets pretty cold. Now with that you're going to run into major humidity issues, because bulbs kill humidity. You need to be careful of using an UTH & heat lamps because if you're not using a thermostat you'll easily kill your snake if something goes wrong, especially with two heating sources. A UTH would help with temperatures, but not so much ambient more than maybe a degree or two. Putting the water bowl over it would help with humidity yes, but then you're heating the drinking source for your snake.
The best way to give you advice is for you to snap a few photos of your setup. Also a PVC cage will work way better and not being open on all sides your snake will likely be much happier. The screen top along with the glass aren't that good for retaining humidity or heat for that matter. Snap a few photos for us though so we can give you better advice.