Grouting my tile?

Not sure if this should be under DIY since I haven't done this yet, but here's my position:

I've been monitoring my tank lately and have noticed that there are severe temperature fluctuations on my ceramic tile. I'm assuming because it is not laying completely flat on the glass to receive proper heating. (Example: I use my temp gun on one part of a hot tile. Without moving toward the cool side, I take the temperature of the same tile on the hot side just 1/4 of an inch away. Between measuring, it ranges from 96ºF and drops to 89ºF. In one quarter of an inch.) On the hot side, still in line with where I originally measured, the edge of the hot side tile that touches the glass of my tank is 84ºF. This is a huge fluctuation for just under a five inch tile (96ºF to 84ºF).

So, since it's obviously the problem because I rearranged my tiles without adjusting my heat, the temperature has become more "even" on just one hot tile (I cut one tile into two pieces for cleaning purposes).

Grouting has become a necessary path. Maybe even getting two full tiles cut instead of four pieces which I might do anyway (some of the tiles are balancing on the glue in the tank, lifting them from the glass surface). So I have a few questions:

1. How quickly does grout dry?
2. Where do I put my gecko if the grout doesn't dry quick enough?
3. Grout may have fumes. What grout is the safest?

Well, I think the fluctuations have to do with where in the UTH you are pointing the temp gun. I believe the middle of the UTH is the hottest part, so as you move outwards it will get a bit cooler. But those are quite large fluctuations, so I think grouting would be a good idea.

1. Depending on the grout brand I think it can take 24-48 hours. It will probably say on the container.
2. Do you have a large tupperware container or storage bin you could keep him in? I use 5litre tupperware containers (long ones) for QT or traveling. There are also those critter keepers you can use. Storage bins are another idea. They are quite big.
3. I think once the grout is dry, there won't be any fumes. But I'm not positive. If you aired it out for a bit I'm sure it would be fine though. Get confirmation on that though! Again, it may say on the package of the grout.