Re: Retired Texas TI99/4A engineer needs help please.
Yes, a 1N4148 will certainly be fast enough. This circuit is unlikely to be running at more than about 20kHz so 'fast' doesn't mean crazy fast, just not absurdly slow like the 1N4007.
TIP31A should be OK running hot but I wouldn't expect it to run really hot here unless you can see signs that it's run hot for a long time in the past. It will get quite warm because it will switch fairly slowly (by modern MOSFET standards) and so be quite wasteful of power.
See if getting the diode sorted out improves matters. It may do.
Chris
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