In my textbook, I have learnt that the First Law of Thermodynamics states
$$ΔU = Q - W$$
where $Q$ is the heat energy applied to the system, $W$ is the work done by the system on its surroundings, and $ΔU$ is the change in the total internal energy of the object.

I have learnt that $U$ includes all forms of energy, including translational/vibrational/rotational KE and PE. Additionally, temperature is determined only by translational KE.

However, excercises in my textbook make it out to seem that an increase in $U$ (whether via work or heat energy) always results in an increase in temperature as well. I do not understand how this can be if $U$ includes forms of energy not counted in temperature. How can work done on an object (e.g. accelerating it with a constant force over some distance in a vacuum) increase the random translational KE of its atoms?

An additional related question is the following: a rubber band holding 5J of elastic potential is released, converting the EPE to KE. My textbook states that in this case $W = -5J$ and this results in an increase of 5J in $U$. However, in my understanding $U$ includes both PE and KE, so if PE was converted into KE there should be no change in $U$.

What am I misinterpreting about the nature of $U$ and the relationship between temperature and $ΔU$?