Background: Relative-tachycardia (RT), a phenomenon of unproportionately high heart-rate elevation in response to fever, has been previously attributed to unfavourable outcomes in severe-inflammatory-response-syndrome (SIRS). Relative heart-rate to body-temperature ratio (RHR) and its prognostic associations in patients with severe and critical coronavirus disease 2019 (COVID-19) have not been investigated. Methods: We retrospectively analyzed heart-rate and body-temperature data at admission in patients who were hospitalized due to COVID-19 at a tertiary center from March 2020 to June 2021. After excluding patients with known heart rate affecting medications (beta-blockers and other antiarrhythmics) and atrial fibrillation, a total of 3490 patients were analyzed. Patients were divided into quartiles based on RHR on admission, with patients belonging to the 1st quartile designated as having relative-bradycardia (RB) and patients belonging to 4th quartile designated as having RT. Comparisons with baseline clinical characteristics and the course of treatment were done. Results: There were 57.5% male patients. Median age was 69 years. Most patients had severe or critical COVID-19 at admission. Median heart-rate at the time of hospital admission was 90/min, median body-temperature was 38 °C, and median RHR was 2.36 with interquartile-range 2.07–2.65. RB in comparison to middle-range RHR was significantly associated with older age, higher comorbidity burden, less severe COVID-19 and less pronounced inflammatory profile, and in comparison to RT additionally with higher frequency of hyperlipoproteinemia but lower frequency of obesity. RT in comparison to middle-range RHR was significantly associated with younger age, more severe COVID-19, lower comorbidity burden, lower frequency of arterial hypertension, higher frequency of diabetes mellitus, and more pronounced inflammatory profile. In multivariate analyses adjusted for clinically meaningful parameters, RB patients experienced more favorable survival compared to RT, whereas RT patients experienced higher mortality in comparison to RB and middle-range RHR patients, independently of older age, male sex, higher comorbidity burden and higher COVID-19 severity. Conclusions: Heart rate and axillary temperature are an indispensable part of a clinical exam, easy to measure, at effectively no cost. RT at admission, as a sign of excessive activation of the sympathetic nervous system, is independently associated with fatal outcomes in COVID-19 patients.