I'm melting!!

Just reached for the controls of my Jolida102 and came away with oozing black slime.   The rubber vibration dampening feet seem all to have melted.   Scraped them off.  Replaced with baby-food container caps.   I assume this will work?    Shouldn't rubber designed for hot amps be able to resist heat?  (or is this just what happens as they age ...)
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It sounds like you may have gotten some kind of chemical on the feet.
Hey this could be a positive, after you have cleaned up the mess of course, these amps really respond very well to a set of Black Diamond Racing Cones #4s, I am running a set under my daughters 302 and a friends amp just like yours if these do not fit the bill try a set of Herbies Tenderfeet.
I had similar thing happen to the rear synthetic feet on my Spectral DMA 360s. They did not get gooey, but did melt and looked like ugly plastic cookies.Came off easy. 

To to upgrade to the new feet, Spectral charged me $900.00. Granted, the amps are 15yrs old but you think Spectral would replace them for free on a $20,000 pair of monoblocks.
Needless to say, I now have Pass Lab XA 160.8s
$900 for four rubber/plastic feet?! A set of Townshend Audio Seismic Isolation Pods cost less than that, and provide real isolation, unlike rubber/plastic feet. 
9 big ones for feet?!  I'm in the wrong business.....we're all in the wrong business....

"...some sort of chemical..."?  I can't think of anything you'd expose your equipment to that would cause that reaction.  Heat, Maybe....but you'd have rode your gear hard and put it up wet to cause that.  That sort of heat would have stressed something else to fail.

That's the sort of thing that Spectral or Jolida should have replaced gratis.  Lousy pick on the part's compound, and that's their screw up.....IMHO....
I can’t explain why, but I know certain types of rubber turn to glue in a few years. I have a Vizio TV and don’t use the remote because I use the cable remote instead. I bought it several years ago and recently found the Vizio remote in a drawer. It stuck to my hand as if it had syrup on it. I recall having similar experience with other remotes in the past so I’m not blaming Vizio, only their choice of coating on the remote.

As to replacement feet for audio equipment. I had good luck with the sorbothane feet available from Audio Advisor. They completely eliminated the external hum from a McIntosh preamp.
Rubbers are noted to react to atmospheric 'additives'...note your car's wiper blades.   Even those are complex compounds...

I'll still stand pat on my observation; the mfr. should send a new set gratis.  They're feet, FGS.  How much can they spend on a set after all?  A 'chump change' item that should be able to be replaced without too much difficulty or a degree in engineering.  Especially when y'all drop that level of cash into the unit....

I'd be annoyed if told that replacements would be a 3 figure charge...light up someone's ear up the food chain over it with the WTF question....;(

But that's me...
This is a drawback of a natural rubber. As all Linn Sondek users know, and I have learned in an unpleasant way! I have pARTicular rack (approved by The Boss!!!) and its a light birch veneer... Melting black rubber totally destroyed it! 
Re. the price of a set of new footers: it is not just us, when I bought a set of new footers for an Eppendorf vacuum-centrifuge for my lab, I thought that I am buying a new centrifuge! But what can a poor boy do? We just pay the price... ;-(