Bash + linux utilities, 19

seq 40 2 72|pv -qlL2

seq generates the numerical output. pv ratelimits it to 2 lines/sec.

Perl 6, 30 bytes

for 20..36 {sleep .5;say 2*$_}

Sorry that it looks like un-golfed code, I don't see a way to make it shorter...

The version that stops right after the last number, would be 37 bytes:

for 20..36 {sleep .5 if $++;say 2*$_}

JavaScript (ES6), 52 bytes

f=(i=40)=>console.log(i)|i-72&&setTimeout(f,500,i+2)

f()

Vim, 24, 23 bytes/keystrokes

i40<esc>qq:sl500m
Yp2<C-a>q15@q

One byte saved thanks to @Kritixi Lithos!

Written from my phone, tested in mobile vim (which is apparently a real thing). I'll post a gif and an explanation later once I have access to a computer.

Mathematica, 34 bytes

Pause[Print@#;.5]&/@Range[40,72,2]

Full program. Takes no input and outputs to STDOUT.

Haskell, 67 bytes

import System.Posix.Unistd
mapM((>>usleep 500000).print)[40,42..70]

If you want to go with ghc only, you can save a few bytes by importing GHC.Conc and using threadDelay instead of usleep.

Perl 6, 27 bytes

sleep .say/2 for 40,42...72

say returns True, which is coerced to a numeric 1 when divided by 2.

MATL, 14 bytes

17:E38+"5&Xx@D

Try it in MATL Online! You may need to reload the page if it doesn't initially work.

Explanation

17:     % Push array [1 2 ... 17]
E       % Multiply by 2, element-wise
38+     % Add 38, element-wise. This gives [40 42 ... 72]
"       % For each k in that array
  5&Xx  %   Pause 0.5 seconds and clear screen
  @D    %   Push k and display
        % End (implicit)

Octave, 38 35 bytes

Saved 3 bytes thanks to @LuisMendo by changing endfor to end

for i=21:36;disp(2*i);sleep(.5);end

Try it online!

I am new to Octave, so this solution still might be golfed further. Any tips are welcome!

Ungolfed

for i=21:36
  disp(2*i)
  sleep(.5)
end

Jelly, 13 12 bytes

40µṄœS.+2µ⁴¡

Try it online! The Jelly prohram is wrapped in a Bash script to prefix each line of output by a timestamp.

How it works

40µṄœS.+2µ⁴¡  Main link. No arguments.

40             Set the return value to 40.
  µ      µ⁴¡  Execute the chain between the two µ 16 times.

After the last iteration, the final value of 72 is printed implicitly and the program exits.

Python 3, 57 56 Bytes

import time
a=40
while a<73:print(a);time.sleep(.5);a+=2

EDIT:

-1 Byte thanks to Mega Man

Common Lisp, 57

(loop for b from 40 do(print b)while(< b 72)do(sleep .5))

Does not sleep after reaching 72.

(loop
  for b from 40
  do (print b)
  while (< b 72)
  do (sleep .5))

php, 38 bytes

for(;35>$t+=2;usleep(5e5))echo$t+38,_;

uses underscore as delimiter. Run with -nr.

QBIC, 21 bytes

[44,72,4|?a $sleep 1.

QBIC starts a FOR-loop, running from 44 to 72 and incrementing the counter by 4 on every loop. Ith then sleeps for 1 second. QBasic doesn't have a more finegrained control foor sleep, so I've added a . to simulate giving .5 as an argument.

Racket 44 bytes

(for((i(range 40 73)))(println i)(sleep .5))

Ungolfed:

(define (f1)
  (for ((i (range 40 73)))
    (println i)
    (sleep .5)))

Testing:

(f)

Output:

40
41
42
43
44
45
...
71
72

R, 49 bytes

x=38;while(x<72){Sys.sleep(.5);x=x+2;cat(x,"\n")}

Very trivial solution but it does the trick.

Clojure, 54 bytes

(doseq[t(range 32 73 2)](println t)(Thread/sleep 500))

Third lisp ftw. Just iterates over the range, printing and sleeping each iteration. Sleeps at the end.

Ungolfed:

(doseq [t (range 32 73 2)]
    (println t)
    (Thread/sleep 500)))

A version that doesn't sleep at the end, 66 bytes

(doseq[t(range 32 73 2)](println t)(if(< t 72)(Thread/sleep 500)))

Note, these are full programs since the instructions don't specify. Add a byte to each if a function is required.

*><>, 20 bytes

"H&"v
?;5S>2+:n:{:}=

Try it here!

This outputs the 40 and adds two every 500ms, outputting the new number. At 72 the program does not wait and exits immediately. Wasn't sure if we needed any sort of deliminator in-between the temperatures so there isn't one included.

Explanation

Setup:

"J("   push 72 and 38 (temp) to the stack
    v  enter main loop at ">"

Main loop:

>               move the IP right
 2+             add two to temp
   :n           copy and output temp
     :{:}       copy temp and 72
         =?;    if temp == 72, exit
            5S  sleep 500ms

TI-Basic (CE or CSE only), 8 bytes

:For(A,42,72
:Pause A,.4
:End

Note that many commands are single byte tokens.