Cancer in myogenic heart cells?
As a preface, this isn't a comprehensive answer for everything. As MattDMo points out, some of the original answer was poor in it's presentation. In my update there's some supporting information to some expert testimonial, but this is mainly targeted at adult cases rather than pediatric cases, i.e. why would cardiac cancer be rare in an adult with no prior history of cancer. There's a reference #5 at the bottom which goes into some of the genetic conditions that result in rhabdomyocarcoma.
Cardiac muscle cells do not divide particularly often (though they may divide: Evidence for cardiomyocyte renewal in humans). This would be a good mechanism of resistance of heart tissue to a more typical or rapid cancer development, compared to say, the endothelium of a vessel or an interstitial/connective tissue cell. Not to say heart tumors are impossible, either, as rhabdomyocarcoma is a good example of a cardiac tumor. Moreover, here's an excerpt from this article on heart cancer:

“There’s not a lot of fatty tissue [in the heart],” Gaynor said. Even more, “the heart’s enclosed in a membrane,” he explained. Known as the pericardium, this fluid-filled sac may itself become engulfed by cancer, with tumors metastasizing to the outside of it, but still it does its job of protecting our precious hearts.
So, even though cancer can happen anywhere there are cells, your heart remains virtually immune due to its muscular nature and the assistance of the pericardium. Smart heart.

And then from Cancer Prognosis: Role of BMI and Fat Tissue,

Many prospective clinical trials have linked excess body weight—typically represented as a BMI of 25kg/m2 of body surface area or greater—with a higher risk of development of cancers, including postmenopausal breast cancer in women and esophageal, colon, pancreatic, endometrial, and kidney cancers in both sexes. The number of obese Americans will increase by an estimated 65 million by 2030, increasing cancer diagnoses by 500,000 (Lancet 2011;378:815–25).

So fat content has it's role in progressing cancers, determinately. Let's explore this part. The adipocyte isn't simply a storage for fat, it has it's own host of proteins it produces and secretes. In obesity, the adipose tissue becomes dysregulated in it's secretion of adipokines [1]. The book Adipose Tissue and Cancer by M. Kolonin, the author notes that two major adipokines, leptin and adiponectin, play a major role in tumorigenesis by induction of cell survival and proliferation pathways [2]. Also duly noted, increased circulating insulin and insulin-like growth factors due to insulin resistance results in mitogenic effects on tumor cells.
White adipose tissue has been shown by Pedro et al. to increase bioavailability of sex hormones such as estradiol, through increased aromatase activity and  &quot;increased insulin and bioactive IGF-1 levels which downregulate the concentration of the circulating sex hormone-binding globulin, resulting in an increased fraction of bioavailable estradiol, but decreased testosterone production.&quot; The same study has a section on inflammation induced by adipose tissue in section 3.2, the entire article is rather long but they sum up some of the information into a figure,

Source: Pedro et al.
Generally speaking, and in reference to the expert testimonial above from Dr. Gaynor, the heart isn't a very fatty organ, and it's protected from the surrounding adipose tissue by the pericardium. You could also argue that the fast flow of blood through the heart would leave a smaller fraction of circulating tumorigenic molecules for ready uptake by cardiac cells.
Being said, and while I haven't any data for the molecular pathogenesis for cardiac tumors, nondividing epidermal cells have been shown to enter a proliferative state in response to inflammation [3]. We also see that adipokines have been implicated in heart disease due to pro-inflammatory effects [4]. My concession here is that the rarity of cancers in adult cardiac muscle cells is because this process is very slow, and it's aided in part by the sort of environment the heart finds itself in. We often see cases of cardiac tumors in children due to errors in development [5].