Onalespib in Treating Patients With Locoregionally Advanced Squamous Cell Carcinoma of the Head and Neck Receiving Radiation Therapy and Cisplatin

Inclusion Criteria: * Patients must have a histologically or cytologically confirmed, previously untreated squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx, or larynx * Tumors must be staged T1-4, N2b-3, M0 (human papillomavirus positive \[HPV\]+ or HPV negative \[-\]); patients with HPV+ tumors should have at least one high risk feature such as T4, N3, or smoking history of \> 10 pack years * The disease must be considered to be potentially curable by combined radiotherapy and cisplatin based chemotherapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Life expectancy of greater than 6 months * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Hemoglobin \>= 9 g/dL * Platelets \>= 100 x 10\^9/L * Serum creatinine =\< 1.5 mg/dL (=\< 120 umol/L) OR calculated creatinine clearance (Cockcroft-Gault formula) \>= 50 mL/min OR 24-hour urine creatinine clearance \>= 50 mL/min * Bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) =\< 2.5 x ULN * Alanine aminotransferase (ALT) =\< 2.5 x ULN * Proteinuria =\< +1 on dipstick or =\< 1 gram/24 hours * Corrected QT using the Fridericia formula (QTcF) \< 470 msec * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, during the study participation, and for three months after the last dose of the drug; women of child-bearing potential must have a negative serum pregnancy test within 14 days prior to registration and agree to use effective contraception throughout the treatment period and for 3 months after the last dose of study treatment; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception; males should avoid fathering children during and for at least three months after therapy is completed * Ability to understand and the willingness to sign a written informed consent document * Available for long-term follow-up of their disease after treatment Exclusion Criteria: * Patients with nasopharyngeal, paranasal sinus, skin, or unknown primary site disease * Presence of distance metastases (M1) * History of another malignancy; exception: patients who have been disease-free for \> 3 years, or patients with a history of completely resected non-melanoma skin cancer and/or patients with indolent secondary malignancies, are eligible; consult the Cancer Therapy Evaluation Program (CTEP) Medical Monitor if unsure whether second malignancies meet the requirements specified above * Previous head and neck radiation therapy * Symptomatic peripheral neuropathy \> grade 2 by Common Terminology Criteria for Adverse Events (CTCAE) criteria * Clinically significant sensorineural hearing impairment which may be worsened via cisplatin exposure (audiometric abnormalities without corresponding clinical deafness are not grounds for exclusion) * Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to AT13387 * Current use of a prohibited medication; the following medications or non-drug therapies are prohibited: the concurrent use of all herbal supplements is prohibited during the study (including, but not limited to, St. John's wort, kava, ephedra \[ma huang\], ginkgo biloba, dehydroepiandrosterone \[DHEA\], yohimbe, saw palmetto, or ginseng) * History or current evidence/risk of visual loss syndromes, including but not limited to retinal vein occlusion (RVO), retinal detachment, macular degeneration, or visual migraine headaches * History or evidence of cardiovascular risk including any of the following: * History or evidence of current clinically significant uncontrolled arrhythmias (exception: patients with controlled atrial fibrillation for \> 30 days prior to randomization are eligible) * History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to randomization * History or evidence of current \>= class II congestive heart failure as defined by the New York Heart Association (NYHA) functional classification system * Treatment-refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mmHg which cannot be controlled by anti-hypertensive therapy * Patients with intra-cardiac defibrillators * Known hepatitis B virus (HBV), or hepatitis C virus (HCV) infection (patients with chronic or cleared HBV and HCV infection are eligible); patients with known human immunodeficiency virus (HIV) infection are eligible if not on antiviral agents and cluster of differentiation (CD)4 counts are adequate (\>= 500) * HIV-positive patients on combination antiretroviral therapy are ineligible * Uncontrolled inter-current illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Any condition or medical problem in addition to the underlying malignancy and organ dysfunction which the investigator feels would pose unacceptable risk * Breastfeeding patients are ineligible