Would these two transistors have the same Beta?
It is not possible to say without component values.  The Beta will vary as a function of collector current.  If their collector currents are the same they would have the same nominal Beta.  Beta has a pretty wide range around the nominal.  If their bias currents are different, then they would have a different nominal Betas.  The data sheet will have a graph that shows the nominal Beta as a function of collector current.


To answer your question, the beta of a transistor also varies this temperature, which you can see in the graph, and with Vce.