A Comprehensive Photometric Selection of `Little Red Dots' in MIRI Fields: An IR-Bright LRD at $z=3.1386$ with Warm Dust Emission

JWST has revealed a population of compact `Little Red Dots' (LRDs) at $z\gtrsim4$, with red rest-frame optical and blue UV colors. These objects are likely compact dusty starbursts or heavily reddened AGNs, playing a pivotal role in early black hole growth, dust production, and stellar assembly. We introduce a new photometric selection to identify LRDs over a broad range in redshifts and rest-frame UV-to-NIR colors enabling a more complete census of the population. This method identifies 248 LRDs with F444W$<27$ mag over 263 arcmin$^2$ in the JADES, PRIMER-COSMOS, and UDS fields with MIRI coverage, increasing the number density by $\times$1.7 compared to previous samples, suggesting that previous census were underestimated. Most LRDs are detected in MIRI/F770W but only 7% (17) are detected in F1800W. We use MIRI-based rest-frame [1$-$3 $\mu$m] colors to trace dust emission. F1800W-detected LRDs have a median [1$-$3 $\mu$m]$=1.5$ mag, with a broad scatter indicative of diverse dust emission properties. About 20% exhibit [1$-$3 $\mu$m]$<1$ mag colors consistent with negligible dust emission, but the majority show significant dust emission at 3 $\mu$m (f$^{\rm dust}_{3\mu m}\lesssim0.8$) from the galaxy ISM or a hot-dust-deficient AGN torus. A correlation between bluer UV-to-NIR colors and stronger IR emission suggests that the bluest LRDs may resemble unobscured QSOs. We report a LRD at $z_{\rm spec}=3.1386$, detected in MIRI, Spitzer/MIPS, and Herschel/PACS. Its IR SED rises steeply at $\lambda_{\rm rest}>6~\mu$m and peaks near $\sim40~\mu$m, providing the first direct evidence of warm dust emission (T$=50-100$ K) in a LRD.