Edit values in a txt file with sed / awk / grep command

Here's a slightly more idiomatic AWK variant to process current.txt (steve's second answer is even more idiomatic!):

awk '/^To(|min|max) / { print $1, $2 + 1; next } 1' current.txt

This looks for lines starting with To, followed by nothing, min, or max, followed by a space; for matching lines it prints the first field and the second field, incremented, separated by the default output field separator (space). Then it skips to the next line. All other lines are printed as-is (1 is a shortcut for this in AWK).

Note that overwriting the file with the new values is probably not a good idea: you won't know whether the values have been corrected or not... If you retrieve the file from the device every time then that doesn't apply.

The same reasoning applies to ws2308.log, so let's just process it in its entirety every time:

$ awk 'NF >= 5 { $5 = $5 + 1 } 1' ws2308.log
20161203150600 2016-Dec-03 15:06:00 11.8 -0.1 -3.2 65 87 0.0 157.5 SSE -1.1 569.80 1015.700
20161203152100 2016-Dec-03 15:21:00 12.3 -0.1 -3.2 64 87 0.0 157.5 SSE -1.1 569.80 1015.600
20161203153600 2016-Dec-03 15:36:00 12.2 -0.2 -3.3 64 87 0.0 135.0 SE -1.2 569.80 1015.700

If you want only the last line:

$ awk 'NF >= 5 { $5 = $5 + 1; lastline = $0 } END { print lastline }' ws2308.log
20161203153600 2016-Dec-03 15:36:00 12.2 -0.2 -3.3 64 87 0.0 135.0 SE -1.2 569.80 1015.700

or if you want the file with only the last line changed:

$ awk 'length(prevline) > 0 { print prevline } NF >= 5 { prevline = $0; $5 = $5 + 1; lastline = $0 } END { print lastline }' ws2308.log
20161203150600 2016-Dec-03 15:06:00 11.8 -1.1 -3.2 65 87 0.0 157.5 SSE -1.1 569.80 1015.700 
20161203152100 2016-Dec-03 15:21:00 12.3 -1.1 -3.2 64 87 0.0 157.5 SSE -1.1 569.80 1015.600 
20161203153600 2016-Dec-03 15:36:00 12.2 -0.2 -3.3 64 87 0.0 135.0 SE -1.2 569.80 1015.700

Here's one solution. For any lines which start with "To", "Tomin" or "Tomax" followed by a space, print the first field and then the second field incremented by 1. Otherwise, just print the full line.

$ awk '{if(/^(To|Tomin|Tomax) /){print $1 " " $2+1}else{print $0}}' w.txt
Date 2016-Dec-03
Time 10:30:29
Ti 11.9
Timin 11.6
Timax 27.7
TTin 10:34
DTimin 2016-01-19
TTimax 00:44
DTimax 2016-08-28
To -1.4
Tomin -3.8
Tomax 38.4
TTomin 06:46
DTomin 2016-02-18
TTomax 16:13
DTomax 2016-07-19
$

Another approach, slightly golfed.

$ awk '/^To/{$2++}1' w.txt
Date 2016-Dec-03
Time 10:30:29
Ti 11.9
Timin 11.6
Timax 27.7
TTin 10:34
DTimin 2016-01-19
TTimax 00:44
DTimax 2016-08-28
To -1.4
Tomin -3.8
Tomax 38.4
TTomin 06:46
DTomin 2016-02-18
TTomax 16:13
DTomax 2016-07-19
$