Can I really boost calorie burning at rest?

Yes, adding lean body mass through progressive resistance training can help boost calorie burn at rest. Additionally, there are natural and synthetic compounds that can slightly increase resting metabolic rate (RMR), which is the amount of calories you burn while awake but sitting quietly. Caffeine is the most common compound used to increase RMR and has been shown to increase energy expenditure (EE) approximately 3-5% in the first 2.5 hours after ingestion. Comparable increases in EE have been shown with Epigallocatechin gallate (EGCG) a compound found it green tea. Combining caffeine and EGCG together, as found in some weight loss supplements, may have a synergistic effect on 24 hour EE. Note that some of the increase in the total 24 Hour EE may also come from the ability of caffeine/EGCG to induce more daily movement, whether it be through fidgeting at rest or simply from an increased desire to move more because of feeling more energetic.

Capsaicin from Cayenne fruit can may also increase RMR by stimulating the sympathetic nervous system (SNS) activity, promoting the secretion of catecholamine (epinephrine and norepinephrine, which increases metabolic rate and temperature), and increasing the expression of the uncoupling protein (UCP) in many tissues leading to an increase in wasting calories as heat. These natural substances are the most well established for increasing REE and thus used in many weight loss supplements but not necessarily in the right doses. They need to be in the proper amounts (depending on a person's size) in order to be effective. A typical proper does is 150-300 mg of caffeine, 10 mg of capsaicin and 270 mg of EGCG. There are a few other natural ingredients that may increase RMR such as bitter orange, but it may pose greater risks. You shouldn't use any of these products if you have adverse reactions to stimulants.