I bet Chilled would get easily offended by certain things. Mainly things that involve an attempt/intent at mocking or making fun of him. He did seem a bit more like a child-ish adult in the Bardock special compared to Frieza, after all.
But anywho, because of this, I can see there being times where Bardock has to provide Chilled with attempted comfort if the Ice-jin ends up having a bit of rough day for what ever reason.
Things like stroking his little horns, simply holding him in your lap if he's willing, making him a soothing bath, or even reminding him of his qualities- preferably as an emperor/tyrant as he thinks of himself as, are ways that could help him settle. Of course, providing him with his more emperor-like qualities is something that Bardock would probably take a bit less seriously and use it as a small chance to poke a bit of annoyance out of Chilled to rile him up more for the heck of it. Bardock finds it amusing to see him kinda get all steamed for no reason, but he doesn't really intend any harm.
I see Chilldock as one of those couples where one of the partners likes to stirr their significant other up a bit just as a way to poke some fun, before they comfort them and calm them down if their joking is taken too seriously.
Like, for example, Bardock saying something like, "You know, for a supposed emperor of high rank, I don't see any high stature on your part." (In other words, Bardock is not only joking about/lightly mocking Chilled's height, but also his royal status in a way that sounds like he doubts it)
And then poor Chilled might ask him to repeat what he just said in a daring tone or something, and Bardock probably repeats himself or goes, "You heard me, Chilly~", using a little nickname and speaking in a sort of smooth voice to press at Chilled even further as though he's testing his luck. Chilled may get flustered at the use of a nickname and stammer, trying to act defensively without much success until Bardock sighs, picks him up in his arms, and just holds him close to calm him because he knows Chilled will allow it, even if reluctantly.
