Tempering chocolate: ± 2 °C too much?

Yes, it is too much. Chocolate has very tight working intervals. Dark chocolate must be used at 32°C. Below 30°C, it is too thick for use, and at 35°C, the cocoa butter separates from the chocolate. An error interval of 4°C when your complete workable interval is 5°C wide is simply unacceptable. You want a thermometer with a much higher precision, actually one which shows you tenths of degrees centigrade.

You also want a thermometer which reacts quickly enough. If you are working with small quantities, a ten seconds delay in measuring can give you errors of over half a degree centigrade, which is also a lot, given your tight working interval. Try finding a thermometer with a 4 sec response time or less.

Also, you don't want a laser thermometer at all! The difference in temperature between the surface of the chocolate and the mass of it near the bottom can be substantial, I once measured 4°C difference in something in a bowl with about a litter of stuff (it can't have been chocolate, probably it was custard, I forgot exactly). You need a candy thermometer for chocolate. Buy a laser thermometer separately for measuring the surfaces of pans, if you need it.

As a last note a 2°C interval is not 36°F, it is just below 4°F. The formula is 32 + 5/9, so your converter probably meant that when there are 2°C outside, a Fahrenheit thermometer shows 36°F. This is obviously incorrect for calculating intervals.