Extinction in 10 or 20 years would be regarded as being roughly equally bad - since these are small figures - smaller than the lifespan of humans and within their planning horizon. So an evolved creature acting in their genetic self-interest can be expected to regard both outcomes as being roughly equally bad.

In the case of 10 years and universal heat death, most evolved creatures would strongly prefer to avoid immediate extinction, since universal heat death is far outside both their experience and their planning horizon. As a bonus, there may be ways of avoiding the heat death - by creating large new low-entropy regions by using known inflationary processes.