I would be changing the BEB to at least eliminate that problem and give you piece of mind. Your mechanic is not going to fix the engine for free, and he obviously doesn't understand the BEB problems these engines have had.
My old boss's HDJ80 was making some ticking noises like these and he also had bubbles in the radiator. Sorry, I left before the problem was solved.
The 1HD T and 1HZ engines have long had mysterious ticking sounds . My HZJ75 had something similar to yours where it would start about 10-15 mins when it got warm. It never got loud and was there for 120000klms while I owned the car. I had the BEB changed as a precaution but the old ones were in perfect condition at 230000klms.