The trend in each of these is important. For global temperature, there are of course models that would indicate global temperature should be increasing with atmospheric CO2 concentrations; with health spending, the underlying theory is less developed, but the implications of changes in health care costs for US government spending and deficits are immense.
For each issue -- global temperature and health spending -- the most recent data observations give rise to speculation on changes in the underlying trend. For instance, here is a headline on health spending, from this Bloomberg story:
Meanwhile on the global temperature issue, we have all kinds of headlines on whether global warming has "stopped" in the last 15 or so years. Here is one example of a headline, from the Guardian in the UK:
However, I will go out on some ice and make an observation: The liberal media has been all over the "marked slowdown" in health care costs as if it is for-sure a real change, while they are all over the "slowdown in global climate change" as either an artifact of starting point or as statistically insignificant.
I think the truth on both is closer to "it's too early to tell."