If the speed of light were faster, it would have significant effects on our understanding of the universe and the laws of physics. It is impossible to say for certain what the consequences would be, but it is likely that the sun's output would increase significantly. However, it is important to note that the speed of light is not directly related to the sun's output. The sun's energy output is determined by its mass and composition, not the speed of light.
As for time travel, it is a highly speculative concept and there is no scientific evidence to support its possibility. The idea of traveling faster than the speed of light, whether it is in the past or the future, remains purely hypothetical. Additionally, even if the speed of light were faster, it is unlikely that it would have any effect on the concept of time travel. Time is a fundamental dimension in our universe and it is not dependent on the speed of light.
In regards to the concern about incineration, it is important to understand that the speed of light is not a measure of temperature. The speed of light is a fundamental constant that is related to the fabric of space-time, not temperature. Therefore, even if the speed of light were faster, it would not necessarily result in a higher temperature or incineration for a time traveler.
In conclusion, while it is interesting to speculate about the effects of a faster speed of light, it is important to remember that it is purely theoretical and has no basis in scientific fact. Time travel, in any form, remains a subject of science fiction and is not supported by current scientific understanding.