Inclusion Criteria:

* Feasibility Phase: Patients must be \< 21 years of age at the time of enrollment; please note: the feasibility phase is complete, effective with amendment #1
* Efficacy Phase: Patients must be =\< 40 years of age at the time of enrollment
* Patients with newly diagnosed RMS of any subtype, except adult-type pleomorphic, based upon institutional histopathologic classification, are eligible to enroll on the study based upon stage, group, and age, as below
* RMS types included under embryonal rhabdomyosarcoma (ERMS) include those classified in the 1995 International Classification of Rhabdomyosarcoma (ICR) as ERMS (classic, spindle cell, and botryoid variants), which are reclassified in the 2013 World Health Organization (WHO) classification as ERMS (classic, dense and botryoid variants) and spindle cell/sclerosing RMS (encompassing the historical spindle cell ERMS variant and the newly recognized sclerosing RMS variant); classification of alveolar rhabdomyosarcoma (ARMS) in the 2013 WHO classification is the same as in the ICR and includes classic and solid variants

* ERMS

* Stage 1, group III (non-orbit)
* Stage 3, group I/II
* Stage 2/3, group III
* Stage 4, group IV, \< 10 years old
* ARMS:

* Stages 1-3, groups I-III
* Specimen Submission: Patients must have sufficient tissue available for the required biology study
* Lansky performance status score \>= 50 for patients =\< 16 years of age; Karnofsky performance status score \>= 50 for patients \> 16 years of age
* Peripheral absolute neutrophil count (ANC) \>= 750/uL
* Platelet count \>= 75,000/uL
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows:

* 1 month to \< 6 months old: 0.4 mg/dl (male), 0.4 mg/dl (female)
* 6 months to \< 1 year old: 0.5 mg/dl (male), 0.5 mg/dl (female)
* 1 to \< 2 years old: 0.6 mg/dl (male), 0.6 mg/dl (female)
* 2 to \< 6 years old: 0.8 mg/dl (male), 0.8 mg/dl (female)
* 6 to \< 10 years old: 1 mg/dl (male), 1 mg/dl (female)
* 10 to \< 13 years old: 1.2 mg/dl (male), 1.2 mg/dl (female)
* 13 to \< 16 years old: 1.5 mg/dl (male), 1.4 mg/dl (female)
* \>= 16 years old: 1.7 mg/dl (male), 1.4 mg/dl (female)
* Patients with an elevated serum creatinine due to obstructive hydronephrosis secondary to tumor are still eligible; however, patients with urinary tract obstruction by tumor must have unimpeded urinary flow established via diversion (i.e. percutaneous nephrostomies or ureteric stents) of the urinary tract
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age
* All patients and/or their parents or legal guardians must sign a written informed consent.
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met.

Exclusion Criteria:

* Patients who have previously received temsirolimus, another mTOR inhibitor, or any other investigational agent
* Patients who have received any chemotherapy (excluding steroids) and/or RT prior to this enrollment
* Patients with uncontrolled hyperglycemia
* Patients with uncontrolled hyperlipidemia
* Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of their study participation and for at least 3 months after treatment is completed
* Female patients who are pregnant are not eligible since fetal toxicities or teratogenic effects have been noted for several of the study drugs; Note: A pregnancy test is required for female patients of childbearing potential prior to study entry
* Lactating females who plan to breastfeed their infants are not eligible