Clarify that question. I'm not sure what you're asking me. You're saying one of two things:

1) If the sun suddenly flared up so much that it began to burn the planet, and then the heat died down, would the climate on Earth remain changed by that sudden burst of heat? Answer: uh...yeah. That's kind of a given. The planet would be dead.

2) If the sun suddenly burnt out completely, would that have a permanent effect on the Earth's climate. Answer: uh...yeah. The planet would freeze.