CLUSTERS OF GALAXIES CONTAIN HOT X-RAY EMITTING GAS AND A POPULATION OF RELATIVISTIC ELECTRONS THAT MAY ALSO BE DETECTABLE AT HARD XRAY ENERGIES. MEASURING THE EMISSION FROM THESE ELECTRONS CAN ANSWER KEY QUESTIONS ABOUT THE FORMATION HISTORY OF CLUSTERS AND THE ENVIRONMENT IN WHICH THE THERMAL GAS RESIDES. IN SEVERAL CLUSTERS THIS EMISSION -- CALLED INVERSE COMPTON OR IC EMISSION -- HAS BEEN CLAIMED TO BE DETECTED WITH A PREVIOUS GENERATION OF X-RAY TELESCOPES BUT THESE DETECTIONS HAVE BEEN DIFFICULT TO CONFIRM AND MAY PROVE TO HAVE BEEN SPURIOUS. THESE RELATIVISTIC ELECTRONS ARE ALMOST CERTAINLY GENERATED DURING CLUSTER-CLUSTER MERGERS ACCELERATED AT SHOCK FRONTS WHERE THE GAS IS ALSO HEATED. PRECISE MEASUREMENTS OF THE POST-SHOCK TEMPERATURE ARE SENSITIVE PROBES OF THE IMPACT VELOCITY OF THE MERGER AND HEATING AND ACCELERATION MECHANISMS AT THE SHOCK. HOWEVER THESE TEMPERATURES TEND TO BE QUITE HIGH AND DIFFICULT FOR FACILITIES LIKE CHANDRA AND XMM-NEWTON TO CONSTRAIN. NUSTAR ALTERNATIVELY HAS THE HIGH ENERGY SENSITIVITY NECESSARY TO NOT ONLY MEASURE THESE TEMPERATURES BUT DETECT IC EMISSION IF IT IS BRIGHT ENOUGH. IN THE CLUSTER ABELL 665 SUCH A SHOCK HAS RECENTLY BEEN DETECTED WITH CHANDRA. OUR UPCOMING NUSTAR OBSERVATION OF BOTH THE SHOCK AND THE REST OF THE CLUSTER WILL MORE PRECISELY MEASURE THE TEMPERATURE HERE AND WILL ALLOW A CLUSTER-WIDE SEARCH FOR IC EMISSION PROVIDING THE MOST SENSITIVE IC CONSTRAINTS IN THIS CLUSTER TO DATE. ADDITIONALLY TEMPERATURE VARIATIONS IN THE HOT GAS OF THE CENTRAL REGIONS OF THE CLUSTER WILL BE MAPPED POTENTIALLY REVEALING DYNAMICAL STRUCTURES DUE TO THE ONGOING CLUSTER-CLUSTER MERGER WHICH ARE THOUGHT TO ACCELERATE THE RELATIVISTIC ELECTRONS IN CLUSTER CENTERS. TO DISTINGUISH THERMAL X-RAYS FROM THE IC EMISSION WE ARE SEARCHING FOR WE MUST ACCURATELY CHARACTERIZE AND MODEL ALL SOURCES OF BACKGROUND INCLUDING SPATIALLY COINCIDENT THERMAL EMISSION AND INSTRUMENTAL AND COSMIC BACKGROUNDS. FOR THE INSTRUMENTAL AND COSMIC BACKGROUNDS WE CAN MODEL THEIR CONTRIBUTIONS WITH THE NUSKYBGD CODE DEVELOPED BY DR. WIK WHICH IS BASED ON LONG OBSERVATIONS OF BLANK FIELDS (AS PART OF EXTRAGALACTIC SURVEY PROGRAMS). FOR THE THERMAL COMPONENT WE WILL SIMULTANEOUSLY FIT NUSTAR SPECTRA WITH SPECTRA FROM THE COMPARABLY LONG ARCHIVAL CHANDRA OBSERVATION. CHANDRA IS MORE SENSITIVE AT LOWER X-RAY ENERGIES -- WHERE THE THERMAL EMISSION IS DOMINANT -- AND WILL AID THE CONSTRAINT OF THE THERMAL CONTRIBUTION. SOFTWARE FOR JOINTLY FITTING NUSTAR AND CHANDRA SPECTRA HAS BEEN DEVELOPED BY DR. WIK TO PERFORM A SIMILAR MEASUREMENT IN THE BULLET CLUSTER (WIK ET AL. 2016 IN PREP.). ALL MEASUREMENTS AND/OR UPPER LIMITS WILL INCLUDE APPROPRIATE SYSTEMATIC UNCERTAINTIES BASED ON PAST WORK ON NUSTAR OBSERVATIONS (WIK ET AL. 2014 APJ 792 48 AND WIK ET AL. 2014 APJ 797 79). THIS RESEARCH SUPPORTS THE STRATEGIC OBJECTIVE OUTLINED IN THE 2014 NASA STRATEGIC PLAN TO "DISCOVER HOW THE UNIVERSE WORKS EXPLORE HOW IT BEGAN AND EVOLVED AND SEARCH FOR LIFE ON PLANETS AROUND OTHER STARS." SHOCK TEMPERATURES AND IC MEASUREMENTS -- OR LACK THEREOF -- IN GALAXY CLUSTERS CONSTRAIN THE MERGER AND PARTICLE ACCELERATION HISTORY OVER COSMIC TIME AND THE MECHANISMS BY WHICH THE ACCELERATION OCCURS IN THESE DIFFUSE PLASMA ENVIRONMENTS. THESE INSIGHTS COUPLED WITH A MORE COMPLETE PICTURE OF THE MERGER DYNAMICS AND STRUCTURE OF ABELL 665 INFORM HOW MERGER EVENTS CAN BIAS MASS ESTIMATES IN CLUSTER SURVEYS USED TO INFER THE COSMOLOGICAL PARAMETERS GOVERNING CLUSTER AND COSMIC EVOLUTION. LASTLY A SIDE BENEFIT OF THIS WORK IS THE FURTHER DEVELOPMENT AND REFINEMENT OF TOOLS MEANT TO ENABLE THE ANALYSIS OF NON- STANDARD NUSTAR OBSERVATIONS (NAMELY VERY EXTENDED DIFFUSE OBJECTS LIKE GALAXY CLUSTERS) WHICH WILL BE MADE AVAILABLE TO THE COMMUNITY AS THE NUSKYBGD CODE HAS BEEN (VIA GITHUB) IN ORDER TO INCREASE THE SCIENTIFIC RETURN OF THE NUSTAR MISSION.