I tempered a few bars of chocolate yesterday and it was a successful experience. Then I stored the remaining in the fridge. If I liquefy it, is it tempered chocolate and can be used as desired or should I do it all again?
It is certainly safer to re-temper chocolate, but it is possible to melt chocolate without letting it go 'out of temper'. The typical upper bound for working with tempered chocolate is 90 F (32 C) for dark chocolate. Using a double-boiler (or an improvised equivalent), it is possible to melt chocolate to a workable state without going over this temperature.
The short answer is likely that, in many cases, it will be easier to re-temper the chocolate than to protect it from higher temperatures during the melting process.
As a side note, a cool, dark place is a preferable storage environment for tempered chocolate. The fridge's humidity may cause it to bloom (develop light patches or spots due to fat separation).