As DWKraus pointed out when answering said previous question, cell membranes start to dissolve around 45°C, providing an upper limit to the temperature an organism can withstand even if it has plenty of heat shock proteins and topoisomerase V.
However, it's important to note that cell membranes are made of lipid bilayers. The longer a lipid's tail is, the more heat-resistant a bilayer made of that lipid is. Provided that you avoid carbon-to-carbon double bonds - i.e. avoid turning the lipids in the cell membranes into unsaturated fats (see here for the difference; basically, unsaturated fats are when fats have carbon-to-carbon double bonds) - they won't kink up and start behaving like a liquid.
As this source points out in this table:
...there are longer lipids out there, ones that dissolve at higher temperatures than 45°C. And if the diarachidoyl phosphatidylcholine/DAPC in the table, with a dissolution temperature of 64.1°C, isn't enough, you could probably base a lipid bilayer off of some other kind of fatty acid, of which there are many.
Tetracontanoic acid, for instance has a long alkane tail indeed - 40 carbons, well more than the 16 and 18 of dipalmitoyl phosphatidylcholine/DPPC and distearoyl phosphatidylcholine/DSPC. This suggests that a lipid bilayer made of an ester of tetracontanoic acid (all lipids are esters of carboxylic acids and alcohols) would be incredibly heat-resistant, and, moreover, that even longer (and therefore more heat-resistant) lipids could potentially be formed, meaning that cell membranes dissolving would be a non-problem.
Now, the hypothetical organism that has all these adaptions:
- has proteins that can't denature
- is immune to sepsis
- can't have its cell membranes dissolve; if they aren't durable enough to avoid dissolving, just add more alkanes on the end until they are
The question: what's the next problem? After septic shock, proteins denaturing, and cell membranes dissolving are overcome, what's the next overheating-related thing to cause physical harm to/kill this organism? Last I checked, it was up to 45°C - can it get higher?
I considered the ether-based cell membranes of archaea for this, rather than the extra-long-lipided ester-based cell membranes I actually chose, but they have rigidity-related, permeability-related, and transmembrane protein-related issues.
Just for context: this is an eukaryotic, multicellular organism, not an archaea. I would also point out that it runs on Earth biology, and that 100°C is likely an upper limit here, considering water boils at that temperature under standard temperature and pressure.