As DNS points out, many right-of-centre people are concerned about the climate. It's sometimes claimed (for example, by the Adam Smith Institute) that capitalism will innovate solutions if left relatively unregulated. And traditional cultural conservatives apply Edmund Burke's reasoning that we - the living - have a duty towards future generations:
(Reflections on the Revolution in France)But one of the first and most leading principles on which the commonwealth and the laws are consecrated, is lest the temporary possessors and life-renters in it, unmindful of what they have received from their ancestors, or of what is due to their posterity, should act as if they were the entire masters; that they should not think it amongst their rights to cut off the entail, or commit waste on the inheritance, by destroying at their pleasure the whole original fabric of their society; hazarding to leave to those who come after them, a ruin instead of an habitation
He was mainly thinking of political institutions and culture here, but it also applies to the natural environment.
We hear less from their counterparts on the left - Marxists who think that increasing industrialisation and production is desirable because it accelerates the demise of capitalism. Forty years ago, that was almost the default position on the left.
I think the main reason why some on the right are opposed to measures designed to mitigate or avert climate change is that they see such measures as requiring increasing regulation and control of individual freedoms. For them, the right of the individual to make their own choices appear threatened by political control. They refer to "watermelon politics": green on the outside, red on the inside. They fear blundering into an irreversible situation of surveillance, scarcity, and curtailment, or suspect that ecological issues have been hijacked by the unreconstructed Marxists and collectivists that they always feared.