It appears that having our own brane to somehow interact with other branes could give rise to quite an interesting system and that interaction could lead to some observable effects. We consider the question of whether or not these signatures of interaction between the branes can be observed. To answer this question, we investigate the effect induced by the inflaton in the WMAP7 data using the warm inflationary model. In this model, slow-roll and perturbation parameters are given in terms of the inflaton thermal distribution. We show that this distribution depends on the orbital radius of the brane motion under the interaction potential of other branes in extra dimensions. Thus, an enhancement in the brane inflation can be a signature of an orbital motion in extra dimensions, and consequently, some signals of other branes can be detected by observational data. According to experimental data, the $N\simeq 50$ case leads to $n_{\text{s}}\simeq 0.96$, where $N$ and $n_{\text{s}}$ are the number of $e$-folds and the spectral index, respectively. This standard case may be found in the range $0.01<R_{\text{tensor}‐\text{scalar}}<0.22$, where $R_{\text{tensor}‐\text{scalar}}$ is the tensor-scalar ratio. We find that at this point, the radial distance between our brane and another brane is $R={\left(1.5\text{GeV}\right)}^{-1}$ in intermediate and $R={\left(0.02225\text{GeV}\right)}^{-1}$ in logamediate inflation.