|Left: an icon (Ѻ), by Savio Alphanso, for someone who is “warmhearted”, an example of a type of thermal word, a conjunction of the thermodynamic term "heat" and the emotional term "heart", representative of love and or passion. Right: a thermodynamics humor take on the first law, employing a "hottest girl" thermal word like usage; or strong analogy as some would call it.|
The term "thermal word" is a 2002 coining of Mark Blumberg. 
In terms of a human thermodynamics and human chemistry analysis of thermal words or "thermal expressions", the breakdown of some of these terms according to actual physics, chemistry, and thermodynamics can be very difficult and elusive to pin down, in many cases. When a pair is engaged in the “heat of sex” an increase in body temperature will occur, and the term seems to be easily explained; but this is not the the complete picture. When, for instance, one wishes to study the change in enthalpy (heat content) in the course of human chemical reaction of a twenty-year marriage, which is where the true understanding of the heat of the sex (relationship) is to be found, the explanation becomes enormously complicated.
It's cold outside, but between us it's cold in here
To cite one example, in the 2008 song “I Hate This Part”, by the Pussycat Dolls, a couple is driving together, at night, in the winter, with snow outside, not speaking, and the female, who is contemplating breaking up, thinks to herself “it’s cold outside, but between us it’s cold in here.”  Here, we may ask is this purely metaphor or is the song writer intuitively commenting on actual physics? Technically, for a bond to break, such as occurs in a relationship breakup (the breaking of a human chemical bond), the system of the reaction will have to absorb energy from the surroundings to detach the union, through the process of debonding or a dissolution reaction: 
A≡B → A + B
|A 26 Nov 2008 video, by Libb Thims, on the analysis of the thermal word expression “hot for words” of the popular YuTube word etymology channel hosted by Marina Orlova.|
In this sense, we could explain the lyrics as an aspect of the relationship being an endergonic (work energy absorbing) or endothermic (heat absorbing) process.  The term "endothermic" seems most apt to the description of temperature drop between the two human molecules, A and B, in the car. Where, in the context of chemistry, it means the chemical reaction (human chemical reaction) that requires heat to break the bonds “A≡B” of the reactants. Technically, an endothermic transformation is one in which the system receives heat from the surroundings: Q > 0. When the transformation occurs at constant pressure: ΔH > 0; at constant volume ΔU > 0. If the surroundings do not supply heat, an endothermic transformation leads to a drop in the temperature (↓T) of the system. 
Hence, it is reasonable to conclude that when the woman thinks to herself: “between us it’s cold”, as the pair drive silently together in the closed system of the car, the thought is partially rewiring her central nervous system in her mind, and can thus be characterized as an endothermic transformation, and the system is becoming colder than surroundings. A comparative example, is the mixing of barium hydroxide Ba(OH)2 and ammonium thiocyanate NH4SCN wherein a powerful endothermic reaction occurs such that the reacting mixture become so cold that the moisture from the air forms a layer of frost on the outer surface of the beaker.
Experimentally, in context of the song, one should be able to measure the inward flow of heat and a temperature drop in the system of the car (or relationship). What equipment would be needed to measure the temperature drop is a matter of further discussion. An extremely graduated thermometer should be able to detect a temperature drop and what is called a “human reaction calorimeter” should be able to measure the heat flow. 
The following are noted thermal word like quotes:
“In everyone's life, at some time, our inner fire goes out. It is then burst into flame by an encounter with another human being. We should all be thankful for those people who rekindle the inner spirit.”[or]“At times our own light goes out and is rekindled by a spark from another person. Each of us has cause to think with deep gratitude of those who have lighted the flame within us.”— Albert Schweitzer (c.1880), alternative translations (Ѻ)
“The only people for me are the mad ones, the ones who are mad to live, mad to talk, mad to be saved, desirous of everything at the same time, the ones who never yawn or say a commonplace thing, but burn, burn, burn, like fabulous yellow Roman candles exploding like spiders across the stars, and in the middle, you see the blue center-light pop, and everybody goes ahh...”— Jack Kerouac (1957), On the Road (see: tattoo)
“I began to realize how important it was to be an enthusiast in life … if you are interested in something, no matter what it is, go at it at full speed ahead. Embrace it with both arms, hug it, love it and above all become passionate about it. Lukewarm is no good. Hot is no good either. White hot and passionate is the only thing to be.”— Roald Dahl (c.1975)
1. Blumberg, Mark S. (2002). Body Heat: Temperature and Life on Earth (term: thermal words, pg. 11; ch. 7: The Heat of Passion, pgs. 151-70). Harvard University Press.
2. (a) HotorNot.com – Homepage.
(b) Hot or Not – Wikipedia.
(c) HotforWords – YouTube.
3. (a) I Hate This Part – Wikipedia.
(b) I Hate This Part (Lyrics) – Clyrics.com.
4. (a) Thims, Libb. (2007). Human Chemistry (Volume One), (preview), (Google books). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two) (term: "human reaction calorimeter", pg. 431) (preview), (Google books). Morrisville, NC: LuLu.
5. (a) Endothermic – Wikipedia.
(b) Endergonic – Wikipedia.
6. Perrot, Pierre. (1998). A to Z of Thermodynamics (pg. 83). Oxford University Press.
● Cold feet (metaphor) – Wikipedia.