TL;DR: Memt x5, v-shaped warm sound under $20 on AliExpress, small and comfy, you can't go wrong with these.
Chi-fi IEMs with warm sound? Hmm I don't have many warm sounding (doh)... With a V-shaped warm-ish sound and a super comfy fit, the Memt X5 are one of my favourite budget IEMs, but the slightly recessed mids might hold you back. I use them as my workout headphones, and for the price (under 20 bucks) you can't go wrong. The legendary KZ ATE are nice, dark and warm. They sell for under $10. Other notable warm IEMs are the Einsear T2, Tin Audio T515 and KZ ZS3 (these ones are said to improve with the Slater mod, easy to perform).
Warmth aside, some other of my favourite chi-fi IEMs are: Tin Audio T2, TFZ Exclusive 5, Seahf AWK-009, Tennmak Dulcimer, KZ ZS5, Xiaomi Piston 3... I think I might have a problem. And on another subject, a well-known warm headphones (not IEMs) that I love are the Koss Porta Pro. Initially I felt a bit dissapointed, they have a huge treble rolloff, but after some listening I feel like the treble gained a bit of presence (maybe it's just my brain, I'm still a bit skeptical on the burn-in subject) and they sound a bit like a "Lo-Fi HD650".