In the simplest model there are 3 kind of mutations: neutral, positive, negative.

The rate at which neutral mutations accumulate (which really means the number of neutral mutations you'll observe between you and your parent) is roughly constant.

But the rate at which positive and negative mutations accumulate depend a lot on: how positive and negative they are (obviously mutations killing the organism won't accumulate) and how many they are among the total number of possible mutations.

When taking a bacteria adapted to a temperature of 20°C and putting it at 30°C the positive mutations (positive for this new environment) will accumulate very fast, at the beginning, and once the bacteria will be adapted to the new temperature there will be much less possible positive mutations, so their accumulation rate will slow down a lot.