Is the hypothalamus in the Temporal Lobe?
No. It is located above the brainstem and below the thalamus.
In humans, the hypothalamus is generally located below the thalamus, hence the name hypo- (below) -thalamus (chamber). It forms the ventral part of the diencephalon (the caudal portion of the prosencephalon/forebrain).
Image 1: General location of the hypothalamus
Image 2: Nuclei of the hypothalamus
The temporal lobe on the other hand is one of the four major lobes of the cerebral cortex in the mammalian brain. It is located below the lateral fissure and it forms from the embryonic telencephalon (rostral portion of the prosencephalon/forebrain).
Image 3: Temporal lobe (green) from Fig. 728 of Gray’s Anatomy (labels removed)
In this case, since the hypothalamus is formed from the diencephalon while the temporal lobe is formed from the telencephalon, we know that the hypothalamus is not in the temporal lobe.
For more images of an actual brain (with labels), you can visit these websites:
http://library.med.utah.edu/WebPath/HISTHTML/NEURANAT/NEURANCA.html
http://www.anatomie-amsterdam.nl/sub_sites/anatomie-zenuwwerking/123_neuro/start.htm
*All images posted were taken from google and they belong to their rightful owners
