If the pieces are naturally pulling out like that, it appears to be warping as well. The temperatures are certainly contributing to the problem but, in my opinion, there are probably 2 other factors. One being moisture and the other being the quality of construction.
The piece appears to be made of engineered wood. Engineered wood (particle board, press board, or whatever name you prefer to use) is like most other materials in that it has various grades. Some high quality grades and some low quality grades. This appears to be a very porous lower quality grade. Most engineered woods do not hold mechanical fasteners well (nails & screws), so they rely on glue, which is fine when done well. In this case, I would guess the porous engineered wood is retaining moisture along with the heat and breaking down the glue bond and allowing the piece to come apart.
Now that I have bored you nearly to death, what do we do about it. I am assuming you do not want to drive nails or screws through the visible finished surface. You can try gluing it back together but it will need to be clamped tightly and allowed to fully cure. You will need to get in there with a glue brush or strip of cardboard and spread the glue evenly on both surfaces. Perhaps that will hold, (maybe for a year, maybe for ten) and you will have only invested in the very best bottle of glue you can get your hands on. If you can get behind the skirt boards under the top, you may be able to glue in some support blocking, again clamping securely and allowing to fully cure.
If that doesn't work, you may have to invest in a table that is made of materials more resilient to the environment of your conservatory. Best of luck!