Below is the derivation of the fixed-end-forces for a uniformly distributed thermal load (temperature change) applied to all or part of an element. The derivation is performed assuming partial loading, but simplifies to the fully-loaded form if $L_2$ = $L$.
Note that the location of $L_2$ does not matter for the derivation of the thermal fixed-end-forces. Because T is a self-straining load, the forces must be equal and opposite on both sides regardless of where along the element $L_2$ is positioned.