Display "(Cell C4) Cell A2" if Cell C4 contains "HOT" or "WARM"

Here's what I currently have, I'm working on a small sales pipeline:

I need it to look like this in another sheet:

I'm using this code:

=IF(OR('Sponsorship '!C4="HOT",'Sponsorship '!B4="WARM"),'Sponsorship '!A4,"")

I was going to attempt how to get the prefix WARM or HOT appended at a later time, but I'm already facing issues as I can't figure out how to get cells that do not meet either criteria (WARM/HOT) to just move on to the next row, rather than show blank. See image of what i mean:

Your response would be greatly appreciated! Thank you!