Note: this answer responded to a different wording of the question, so the focus is different, but it still responds to the question in its current form.
The answer is, "It depends." This can be answered in only a very generic way.
"Silicone" describes a general class of materials. Within that are various chemistries for curing (e.g., condensation or peroxide), or catalyzing (e.g., platinum or tin), even UV, and wide variations in properties. The effect of heat is different for different curing/catalyzing chemistries, as well as when and how much heat is used during curing. "Two-part" chemistry doesn't narrow it down much as that still includes a variety of curing/catalyzing methods.
Heat during curing
The effect of heat during curing varies. For example, with tin-catalyzed silicone, heat has no effect on the cure. However, excessive heat (and what constitutes "excessive" varies), can degrade the silicone, resulting in lower mechanical properties (whatever those would be in the result).
By contrast, the curing of platinum-catalized silicone is directly affected by heat (20-25% increase in cure rate for roughly every 10°C). Too rapid curing can degrade the physical properties of the result.
In these two examples, the problematic heat range is different, but the effect on both would be degrading the resulting physical properties relative to the characteristics the system was designed to produce.
It isn't clear whether too-rapid curing of platinum-catalized silicone could leave unreacted components trapped in the silicone; or if so, whether those could migrate out and leave a surface residue like you describe in your question on slimy silicone molds. However, properly mixed silicone (that has not expired), will generally cure throughout if given enough time, so I wouldn't place this high on the list of potential causes for your other question.
Heat after curing
Again, this is very affected by the chemistry of the silicone, how much heat it is exposed to, and when in relation to the curing process it happens. But assuming the cure has gone to "completion" (per the manufacturer's instructions), before the silicone is exposed to "excessive" heat, there can be a post-curing effect.
Silicone doesn't reach full cure in the minutes or hours specified on the product. It reaches a "mostly cured" state that is good enough to start using it. The cure continues at a slow rate over a very long time, during which the physical characteristics will change a little. For a chemistry that is affected by heat, a post cure exposure to elevated heat can accelerate that process to reach the final characteristics.
Some chemistries produce by-products or residual materials that remain in the silicone after curing. Some of those materials will migrate out of the silicone over time. Sometimes, this will change the characteristics. For example, the silicone may become less flexible. Also, the by-products may not be good for you, which could be relevant if the use is for a food or medical purpose.
So some silicone products are purposely exposed to heat in a "post-cure" to accelerate that process and get the silicone to its final state and characteristics. The situation described in the question could have a similar effect.
What effect will it have?
Could be no effect, or could be a noticeable effect.
Some kinds of potential effects wouldn't change the characteristics. Assuming you clean the mold, you might never know whether it was affected.
Depending on the chemistry, the physical properties could change a little. Any physical characteristic could change, but recognize that some characteristics wouldn't necessarily affect your usage.
Regarding the example changes mentioned in the question, it would have to be hot enough to scorch the silicone, or remain at the upper end of its temperature range for a prolonged period, for it to become hard and brittle. Warping would not be a likely effect.
But to narrow the range of possibilities, the question describes this as an occupied workspace. Assuming the temperature is in a range tolerable by humans, the likely outcome would be that any effects wouldn't be very noticeable.
Update based on modified question
Exceeding the recommended temperature, whatever that may be for a specific product, by 5-10°C is not a huge temperature difference. Since the temperature in the working area is often poorly controlled and inaccurately measured, it is likely that manufacturers build in a little cushion in their instructions so that if user measurements are slightly off, the product doesn't fail. YMMV on what that buys you for a specific product or chemistry.
As mentioned earlier, some chemistries are unaffected by any temperature in a range tolerable to human users. If those materials have a specified curing temperature range, it is because the manufacturer conducted testing in that range and doesn't want the liability for speculating about temperatures they haven't tested. For those silicones, curing at 5-10°C over the recommendation probably won't have a noticeable affect.
Also as mentioned earlier, some chemistries are directly affected by curing temperature. For platinum-catalized silicone, for example, a 10°C higher temperature will speed up the cure rate by 20-25%. If you are already above the recommended temperature range, speeding up the cure that much could affect the quality of the cure and the resulting physical characteristics. Exactly how that would affect a particular product depends on the product.
Whatever effects result, if any, the speculated problems of becoming hard, brittle, or warped would not likely be among them for any two-part silicone product cured at 5-10°C above the manufacturer's recommendations.
Silicone isn't cheap, and stuff can go wrong for various reasons even when you follow the manufacturer's recommendations. There is also expected wastage as you perfect your processes and techniques for various use cases. If you are going to invest in using it, it makes sense to minimize potential issues by working within the manufacturer's recommendations.
It's your time and money, so if you want to experiment with how a product behaves outside the recommended conditions, have at it. But recognize that you're working with conditions that are unsupported by the manufacturer, and likely not reliably documented by anybody else who might have tried it (unintentionally or intentionally).
Also, the question wording continues to refer to some "generic" two-part silicone, as if that described a specific kind of material. It doesn't. Two-part silicones for mold-making encompass various chemsitries. This question is focused on temperature. The different chemistries react differently to temperature. But more important, they have different considerations for what they're compatible with, and what substances will inhibit or affect curing. That is much more pertinent to using the material effectively, and solving issues that arise. Knowing what curing chemistry the silicone employs is fundamental to using it successfully.